## Zhang, Xiang

Compute Distance To:
 Author ID: zhang.xiang Published as: Zhang, Xiang Homepage: http://math.sjtu.edu.cn/faculty/zhangxiang/Homepage%20English.html External Links: ORCID · ResearchGate
 Documents Indexed: 197 Publications since 1990, including 2 Books 1 Contribution as Editor Reviewing Activity: 32 Reviews Co-Authors: 49 Co-Authors with 100 Joint Publications 2,012 Co-Co-Authors
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### Co-Authors

 48 single-authored 46 Llibre, Jaume 7 Wei, Lijun 7 Yu, Jiang 5 Li, Weigu 4 Cao, Jinlong 4 Chen, Cheng 4 Gasull, Armengol 4 Han, Maoan 4 Pan, Yangyou 4 Romanovski, Valery G. 4 Wu, Kesheng 4 Ye, Qin 3 Edirisinghe, N. Chanaka P. 3 Oskay, Caglar 3 Pi, Dingheng 3 Walcher, Sebastian 2 Brandyberry, David R. 2 Gao, Wen 2 Geubelle, Philippe H. 2 Liang, Haihua 2 Ma, Siwei 2 Tang, Yilei 2 Torregrosa, Joan 2 Valls Anglés, Cláudia 2 Wang, Shiqi 2 Weng, Shiliang 2 Xu, Yuxing 2 Yi, Yingfei 1 ADNI 1 Alshal, Hassan 1 Bai, Yuzhen 1 Baral, Purna C. 1 Beranger, Boris 1 Boyadzhiyska, Simona 1 Chen, Jian 1 Chen, Nathan 1 Chen, Shuhang 1 Chen, Songlin 1 Chen, Xianfeng 1 Chen, Xiu 1 Christopher, Colin J. 1 Coenen, Wilfried 1 Cong, Wang 1 Curtright, Thomas L. 1 Du, Zengji 1 Dutta, Niloy K. 1 Giné, Jaume 1 He, Guowei 1 He, Zecen 1 Huang, Yifan 1 Kruff, Niclas 1 Lange, Karen 1 Léger, Alain 1 Li, Lexin 1 Li, Lingfei 1 Li, Shimin 1 Liang, Feng 1 Lin, Zhouchen 1 Lin, Zixing 1 Liu, Xi 1 Long, Min 1 Lü, Tinghua 1 Mo, Jiaqi 1 Molin, Bernard 1 Nicolau, Marcel 1 Pan, Wenfeng 1 Pantazi, Chara 1 Peng, Fei 1 Ponce, Enrique 1 Pratt, Elaine 1 Qiao, Z. X. 1 Quadrio, Maurizio 1 Rémy, Frédérique 1 Rey, David 1 Saghin, Radu 1 Sánchez, Antonio L. 1 Scanlon, R. 1 Schlomiuk, Dana I. 1 Shen, Dinggang 1 Shen, Jianhe 1 Shen, Xiang 1 Sheng, Lijuan 1 Shi, Hua 1 Shi, Juanrong 1 Sisson, Scott A. 1 Sun, Huifang 1 Sun, Jiarui 1 Tamang, Karan 1 Villadelprat, Jordi 1 Wallbaum, John 1 Wang, Cong 1 Wang, Jinhuan 1 Wang, Long 1 Wang, Shizhao 1 Wang, Weixia 1 Wang, Yiwen 1 Wang, Yueming 1 Wu, Qinkuan 1 Xia, Damin 1 Xia, Yonghui ...and 15 more Co-Authors
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### Serials

 25 Journal of Differential Equations 10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 7 Qualitative Theory of Dynamical Systems 6 Computer Methods in Applied Mechanics and Engineering 6 Nonlinearity 6 Journal of Physics A: Mathematical and General 6 Bulletin des Sciences Mathématiques 5 Discrete and Continuous Dynamical Systems 4 Journal of Fluid Mechanics 4 Journal of Mathematical Physics 4 Proceedings of the American Mathematical Society 4 Applied Mathematics and Mechanics. (English Edition) 4 Physica D 4 Mathematica Applicata 4 Journal of Dynamics and Differential Equations 4 Nonlinear Analysis. Real World Applications 3 Journal of Mathematical Analysis and Applications 3 Annals of Differential Equations 3 European Journal of Operational Research 2 Rocky Mountain Journal of Mathematics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Biometrika 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Pacific Journal of Mathematics 2 Acta Mathematicae Applicatae Sinica 2 Chinese Annals of Mathematics. Series A 2 Chinese Annals of Mathematics. Series B 2 Science in China. Series A 2 Expositiones Mathematicae 2 Journal of Anhui Normal University. Natural Science 2 Acta Mathematica Scientia. Series A. (Chinese Edition) 2 IEEE Transactions on Image Processing 2 Science China. Mathematics 1 Archives of Mechanics 1 Communications in Mathematical Physics 1 European Journal of Physics 1 Houston Journal of Mathematics 1 Scandinavian Journal of Statistics 1 Ukrainian Mathematical Journal 1 Journal of Geometry and Physics 1 Algebra and Logic 1 American Journal of Mathematics 1 Applied Mathematics and Computation 1 Canadian Mathematical Bulletin 1 Journal of Functional Analysis 1 Journal of the Operational Research Society 1 Journal of Optimization Theory and Applications 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Studies in Applied Mathematics 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Journal of Mathematical Research & Exposition 1 Journal of Engineering Mathematics (Xi’an) 1 Acta Mathematicae Applicatae Sinica. English Series 1 Optimization 1 Journal of Jiangxi Normal University. Natural Science Edition 1 Computational Mechanics 1 Applied Mathematics Letters 1 Systems Science and Mathematical Sciences 1 Neural Computation 1 International Journal of Adaptive Control and Signal Processing 1 Dynamic Systems and Applications 1 Journal of Statistical Computation and Simulation 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Chinese Science Bulletin 1 Journal of Nonlinear Science 1 The Canadian Applied Mathematics Quarterly 1 Electronic Journal of Differential Equations (EJDE) 1 Computational and Applied Mathematics 1 Journal of Lie Theory 1 Statistica Sinica 1 Nonlinear Dynamics 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Chinese Quarterly Journal of Mathematics 1 Chaos 1 Acta Mathematica Sinica. English Series 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Systems Science and Complexity 1 SIAM Journal on Applied Dynamical Systems 1 Mediterranean Journal of Mathematics 1 Networks and Spatial Economics 1 Developments in Mathematics 1 Journal of Biological Dynamics 1 Discrete and Continuous Dynamical Systems. Series S 1 IET Control Theory & Applications 1 International Journal of Mathematics in Operational Research 1 Journal of Applied Analysis and Computation 1 Journal of Shanghai Normal University. Natural Sciences
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### Fields

 142 Ordinary differential equations (34-XX) 57 Dynamical systems and ergodic theory (37-XX) 10 Partial differential equations (35-XX) 10 Mechanics of deformable solids (74-XX) 8 Operations research, mathematical programming (90-XX) 8 Biology and other natural sciences (92-XX) 6 Statistics (62-XX) 5 Mechanics of particles and systems (70-XX) 5 Fluid mechanics (76-XX) 4 Integral equations (45-XX) 4 Information and communication theory, circuits (94-XX) 3 Numerical analysis (65-XX) 3 Optics, electromagnetic theory (78-XX) 3 Systems theory; control (93-XX) 2 Number theory (11-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)

### Citations contained in zbMATH Open

137 Publications have been cited 1,240 times in 664 Documents Cited by Year
Darboux theory of integrability in $$\mathbb C^n$$ taking into account the multiplicity. Zbl 1163.34003
Llibre, Jaume; Zhang, Xiang
2009
Bifurcation theory for finitely smooth planar autonomous differential systems. Zbl 1410.34116
Han, Maoan; Sheng, Lijuan; Zhang, Xiang
2018
Invariant algebraic surfaces of the Lorenz system. Zbl 1059.34005
Llibre, Jaume; Zhang, Xiang
2002
Polynomial first integrals for quasi-homogeneous polynomials differential systems. Zbl 1024.34001
Llibre, Jaume; Zhang, Xiang
2002
Darboux theory of integrability for polynomial vector fields in taking into account the multiplicity at infinity. Zbl 1198.34054
Llibre, Jaume; Zhang, Xiang
2009
Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems. Zbl 1301.34055
Liang, Feng; Han, Maoan; Zhang, Xiang
2013
Equivalence of the Melnikov function method and the averaging method. Zbl 1377.34056
Han, Maoan; Romanovski, Valery G.; Zhang, Xiang
2016
Analytic normalization of analytic integrable systems and the embedding flows. Zbl 1141.34004
Zhang, Xiang
2008
Rational first integrals in the Darboux theory of integrability in $$\mathbb C^n$$. Zbl 1190.34003
Llibre, Jaume; Zhang, Xiang
2010
On the Darboux integrability of polynomial differential systems. Zbl 1266.34002
Llibre, Jaume; Zhang, Xiang
2012
Invariant algebraic surfaces of the Rikitake system. Zbl 0967.34002
Llibre, Jaume; Zhang, Xiang
2000
Local first integrals of differential systems and diffeomorphisms. Zbl 1043.37010
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2003
Darboux integrability and invariant algebraic curves for planar polynomial systems. Zbl 1012.34035
Christopher, Colin; Llibre, Jaume; Pantazi, Chara; Zhang, Xiang
2002
Darboux polynomials and algebraic integrability of the Chen system. Zbl 1148.34001
Lü, Tinghua; Zhang, Xiang
2007
The sliding bifurcations in planar piecewise smooth differential systems. Zbl 1290.34047
Pi, Dingheng; Zhang, Xiang
2013
On the differentiability of first integrals of two dimensional flows. Zbl 1010.34023
Li, Weigu; Llibre, Jaume; Nicolau, Marcel; Zhang, Xiang
2002
Extension of Floquet’s theory to nonlinear periodic differential systems and embedding diffeomorphisms in differential flows. Zbl 1048.37018
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2002
Averaging methods of arbitrary order, periodic solutions and integrability. Zbl 1336.34062
Giné, Jaume; Llibre, Jaume; Wu, Kesheng; Zhang, Xiang
2016
Integrability of dynamical systems: algebra and analysis. Zbl 1373.37053
Zhang, Xiang
2017
Analytic integrable systems: analytic normalization and embedding flows. Zbl 1335.34072
Zhang, Xiang
2013
Hopf bifurcation in higher dimensional differential systems via the averaging method. Zbl 1171.34027
Llibre, Jaume; Zhang, Xiang
2009
Canards, heteroclinic and homoclinic orbits for a slow-fast predator-prey model of generalized Holling type III. Zbl 1418.34103
Wang, Cheng; Zhang, Xiang
2019
Liouvillian integrability of polynomial differential systems. Zbl 1331.34006
Zhang, Xiang
2016
On the Hopf-zero bifurcation of the Michelson system. Zbl 1220.34070
Llibre, Jaume; Zhang, Xiang
2011
The 16th Hilbert problem on algebraic limit cycles. Zbl 1365.34064
Zhang, Xiang
2011
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center. Zbl 1411.34030
Llibre, Jaume; Zhang, Xiang
2018
Global structure of quaternion polynomial differential equations. Zbl 1251.34019
Zhang, Xiang
2011
Existence of piecewise linear differential systems with exactly $$n$$ limit cycles for all $$n\in \mathbb N$$. Zbl 1039.34023
Llibre, Jaume; Ponce, Enrique; Zhang, Xiang
2003
Darboux polynomials and rational first integrals of the generalized Lorenz systems. Zbl 1246.34018
Wu, Kesheng; Zhang, Xiang
2012
Dynamics of the Lorenz system having an invariant algebraic surface. Zbl 1152.81361
Cao, Jinlong; Zhang, Xiang
2007
Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces. Zbl 1194.34050
Zhang, Xiang; Llibre, Jaume
2002
Varieties of local integrability of analytic differential systems and their applications. Zbl 1305.34022
Romanovski, Valery G.; Xia, Yonghui; Zhang, Xiang
2014
First integrals and normal forms for germs of analytic vector fields. Zbl 1166.34018
Chen, Jian; Yi, Yingfei; Zhang, Xiang
2008
Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems. Zbl 1334.37051
Wei, Lijun; Zhang, Xiang
2016
On the number of limit cycles for some perturbed Hamiltonian polynomial systems. Zbl 0992.34021
Llibre, Jaume; Zhang, Xiang
2001
One-dimensional quaternion homogeneous polynomial differential equations. Zbl 1223.34060
Gasull, Armengol; Llibre, Jaume; Zhang, Xiang
2009
Limit cycles for discontinuous planar piecewise linear differential systems separated by an algebraic curve. Zbl 1414.34023
Llibre, Jaume; Zhang, Xiang
2019
Local first integrals for systems of differential equations. Zbl 1055.34074
Zhang, Xiang
2003
Center of planar quintic quasi-homogeneous polynomial differential systems. Zbl 1327.34054
Tang, Yilei; Wang, Long; Zhang, Xiang
2015
Darboux integrability for the Rössler system. Zbl 1047.34002
Llibre, Jaume; Zhang, Xiang
2002
A system of generalized Sylvester quaternion matrix equations and its applications. Zbl 1410.15037
Zhang, Xiang
2016
Melnikov functions for period annulus, nondegenerate centers, heteroclinic and homoclinic cycles. Zbl 1052.37015
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2004
Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces. Zbl 1338.37038
Wu, Kesheng; Zhang, Xiang
2013
On the algebraic limit cycles of Liénard systems. Zbl 1158.34021
Llibre, Jaume; Zhang, Xiang
2008
Averaging theory of arbitrary order for piecewise smooth differential systems and its application. Zbl 1387.34069
Wei, Lijun; Zhang, Xiang
2018
Stability loss delay and smoothness of the return map in slow-fast systems. Zbl 1396.34042
Wang, Cheng; Zhang, Xiang
2018
Generalized rational first integrals of analytic differential systems. Zbl 1232.34004
Cong, Wang; Llibre, Jaume; Zhang, Xiang
2011
The hyperelliptic limit cycles of the Liénard systems. Zbl 1208.34038
Yu, Xiaolan; Zhang, Xiang
2011
Invariant algebraic surfaces of the Rabinovich system. Zbl 1066.34027
Xie, Feng; Zhang, Xiang
2003
The topological structure of the Rabinovich system having an invariant algebraic surface. Zbl 1141.34028
Chen, Cheng; Cao, Jinlong; Zhang, Xiang
2008
Relaxation oscillations in a slow-fast modified Leslie-Gower model. Zbl 1433.34069
Wang, Cheng; Zhang, Xiang
2019
Planar analytic vector fields with generalized rational first integrals. Zbl 1032.34029
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2001
On the sliding bifurcation of a class of planar Filippov systems. Zbl 1270.34088
Pi, Dingheng; Yu, Jiang; Zhang, Xiang
2013
Vector fields with homogeneous nonlinearities and many limit cycles. Zbl 1326.34060
Gasull, Armengol; Yu, Jiang; Zhang, Xiang
2015
Exponential factors and Darbouxian first integrals of the Lorenz system. Zbl 1060.34004
Zhang, Xiang
2002
Eigenstrain based reduced order homogenization for polycrystalline materials. Zbl 1423.74796
Zhang, Xiang; Oskay, Caglar
2015
The Chen system having an invariant algebraic surface. Zbl 1165.34357
Cao, Jinlong; Chen, Cheng; Zhang, Xiang
2008
Nonuniform dichotomy spectrum and normal forms for nonautonomous differential systems. Zbl 1306.34083
Zhang, Xiang
2014
The number of polynomial solutions of polynomial Riccati equations. Zbl 1359.34020
Gasull, Armengol; Torregrosa, Joan; Zhang, Xiang
2016
The embedding flows of $$C^\infty$$ hyperbolic diffeomorphisms. Zbl 1221.37101
Zhang, Xiang
2011
Improved coupling of finite element method with material point method based on a particle-to-surface contact algorithm. Zbl 1423.74870
Chen, Z. P.; Qiu, X. M.; Zhang, X.; Lian, Y. P.
2015
Local Darboux first integrals of analytic differential systems. Zbl 1291.34068
Llibre, Jaume; Walcher, Sebastian; Zhang, Xiang
2014
Integrals of motion of the Rabinovich system. Zbl 0962.34034
Zhang, Xiang
2000
Invariant algebraic curves and rational first integrals of holomorphic foliations in $$\mathbb C P(2)$$. Zbl 1217.37049
Zhang, Xiang
2003
Exponential factors and Darboux integrability for the Rössler system. Zbl 1085.34505
Zhang, Xiang
2004
Existence of limit cycles in a multiply-connected region. Zbl 0934.34023
Zhang, Xiang
1999
Polynomial first integrals of quadratic systems. Zbl 1041.34018
Llibre, Jaume; Zhang, Xiang
2001
On polynomial integrability of the Euler equations on $$\mathfrak{so}(4)$$. Zbl 1325.34003
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
2015
The completely integrable differential systems are essentially linear differential systems. Zbl 1332.34004
Llibre, Jaume; Valls, Claudia; Zhang, Xiang
2015
Study of a transition in the qualitative behavior of a simple oscillator with Coulomb friction. Zbl 1279.34064
Pratt, Elaine; Léger, Alain; Zhang, Xiang
2013
On the analytic integrability of the 5-dimensional Lorenz system for the gravity-wave activity. Zbl 1287.34003
Llibre, Jaume; Saghin, Radu; Zhang, Xiang
2014
Varieties and analytic normalizations of partially integrable systems. Zbl 1357.34072
Du, Zengji; Romanovski, Valery G.; Zhang, Xiang
2016
Portfolio selection under DEA-based relative financial strength indicators: Case of US industries. Zbl 1153.90454
Edirisinghe, N. C. P.; Zhang, X.
2008
Quadratic differential systems with complex conjugate invariant lines meeting at a finite point. Zbl 1393.37023
Schlomiuk, Dana; Zhang, Xiang
2018
The period function of Hamiltonian systems with separable variables. Zbl 1451.37085
2020
Normal form and limit cycle bifurcation of piecewise smooth differential systems with a center. Zbl 1344.34029
Wei, Lijun; Zhang, Xiang
2016
Embedding diffeomorphisms in flows in Banach spaces. Zbl 1177.37026
Zhang, Xiang
2009
On natural modes in moonpools and gaps in finite depth. Zbl 1419.76346
Molin, Bernard; Zhang, X.; Huang, H.; Remy, F.
2018
A mesh-grading material point method and its parallelization for problems with localized extreme deformation. Zbl 1423.74901
Lian, Y. P.; Yang, P. F.; Zhang, X.; Zhang, F.; Liu, Y.; Huang, P.
2015
Dynamics of a nonlinear equation modelling the capillary rise. Zbl 1415.34062
Zhang, Xiang
2018
Sparse and scalable eigenstrain-based reduced order homogenization models for polycrystal plasticity. Zbl 1439.74328
Zhang, Xiang; Oskay, Caglar
2017
Constructing likelihood functions for interval-valued random variables. Zbl 1444.62139
Zhang, X.; Beranger, B.; Sisson, S. A.
2020
On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities. Zbl 1296.34076
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
2014
Analytic normalization of analytically integrable differential systems near a periodic orbit. Zbl 1297.34055
Wu, Kesheng; Zhang, Xiang
2014
An algorithm for solving the minimum-norm point problem over the intersection of a polytope and an affine set. Zbl 0986.90028
Fujishige, S.; Liu, Xiaojun; Zhang, X.
2000
Embedding smooth diffeomorphisms in flows. Zbl 1194.37074
Zhang, Xiang
2010
Limit cycles of differential systems via the averaging methods. Zbl 1362.34066
Pi, Dingheng; Zhang, Xiang
2009
A note on local integrability of differential systems. Zbl 1385.34004
Zhang, Xiang
2017
Limit cycles created by piecewise linear centers. Zbl 07067905
Llibre, Jaume; Zhang, Xiang
2019
The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems. Zbl 1430.34039
Llibre, Jaume; Zhang, Xiang
2019
Determination of the sign of divergence of a quadratic system at critical points. Zbl 0911.34024
Zhang, Xiang
1997
Testing conditional mean independence for functional data. Zbl 1441.62108
Lee, C. E.; Zhang, X.; Shao, X.
2020
Piecewise linear differential systems with an algebraic line of separation. Zbl 1440.34032
Gasull, Armengol; Torregrosa, Joan; Zhang, Xiang
2020
Global $${C}^{\infty}$$ integrability of cubic-linear polynomial differential systems. Zbl 1319.34009
Pan, Yangyou; Wang, Cong; Zhang, Xiang
2014
Darboux integrability and algebraic limit cycles for a class of polynomial differential systems. Zbl 1308.34040
Cao, Jinlong; Llibre, Jaume; Zhang, Xiang
2014
On the limit cycles of linear differential systems with homogeneous nonlinearities. Zbl 1337.34034
Llibre, Jaume; Zhang, Xiang
2015
Liouvillian integrability versus Darboux polynomials. Zbl 1364.34016
Llibre, Jaume; Valls, Claudia; Zhang, Xiang
2016
Ergodicity of limit cycles in quadratic systems. Zbl 0979.34025
Zhang, Xiang
2001
Input/output selection in DEA under expert information, with application to financial markets. Zbl 1206.91019
Edirisinghe, N. C. P.; Zhang, X.
2010
Invariant hyperplanes and Darboux integrability of polynomial vector fields. Zbl 1054.34062
Zhang, Xiang
2002
Limit cycles and global dynamics of planar piecewise linear refracting systems of focus-focus type. Zbl 1457.34031
Liang, Haihua; Li, Shimin; Zhang, Xiang
2021
Eighteen limit cycles around two symmetric foci in a cubic planar switching polynomial system. Zbl 1482.34099
Yu, Pei; Han, Maoan; Zhang, Xiang
2021
Polynomial differential equations over the quaternions. Zbl 1466.34036
Walcher, Sebastian; Zhang, Xiang
2021
Complex planar Hamiltonian systems: linearization and dynamics. Zbl 1478.37061
Shi, Hua; Zhang, Xiang; Zhang, Yuyan
2021
Lubrication analysis of peristaltic motion in non-axisymmetric annular tubes. Zbl 07392412
Coenen, W.; Zhang, X.; Sánchez, A. L.
2021
The period function of Hamiltonian systems with separable variables. Zbl 1451.37085
2020
Constructing likelihood functions for interval-valued random variables. Zbl 1444.62139
Zhang, X.; Beranger, B.; Sisson, S. A.
2020
Testing conditional mean independence for functional data. Zbl 1441.62108
Lee, C. E.; Zhang, X.; Shao, X.
2020
Piecewise linear differential systems with an algebraic line of separation. Zbl 1440.34032
Gasull, Armengol; Torregrosa, Joan; Zhang, Xiang
2020
Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems. Zbl 1444.34058
Wei, Lijun; Zhang, Xiang
2020
Envelopes in multivariate regression models with nonlinearity and heteroscedasticity. Zbl 1457.62174
Zhang, X.; Lee, C. E.; Shao, X.
2020
Canards, heteroclinic and homoclinic orbits for a slow-fast predator-prey model of generalized Holling type III. Zbl 1418.34103
Wang, Cheng; Zhang, Xiang
2019
Limit cycles for discontinuous planar piecewise linear differential systems separated by an algebraic curve. Zbl 1414.34023
Llibre, Jaume; Zhang, Xiang
2019
Relaxation oscillations in a slow-fast modified Leslie-Gower model. Zbl 1433.34069
Wang, Cheng; Zhang, Xiang
2019
Limit cycles created by piecewise linear centers. Zbl 07067905
Llibre, Jaume; Zhang, Xiang
2019
The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems. Zbl 1430.34039
Llibre, Jaume; Zhang, Xiang
2019
The conducting ring viewed as a wormhole. Zbl 1421.78009
Curtright, T.; Alshal, H.; Baral, P.; Huang, S.; Liu, J.; Tamang, K.; Zhang, X.; Zhang, Y.
2019
Tensor generalized estimating equations for longitudinal imaging analysis. Zbl 1432.62196
Zhang, Xiang; Li, Lexin; Zhou, Hua; Zhou, Yeqing; Shen, Dinggang; ADNI
2019
Limit cycles of polynomial Liénard systems via the averaging method. Zbl 07030124
Shi, Juanrong; Wang, Weixia; Zhang, Xiang
2019
IGFEM-based shape sensitivity analysis of the transverse failure of a composite laminate. Zbl 1464.74155
Zhang, Xiang; Brandyberry, David R.; Geubelle, Philippe H.
2019
Bifurcation theory for finitely smooth planar autonomous differential systems. Zbl 1410.34116
Han, Maoan; Sheng, Lijuan; Zhang, Xiang
2018
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center. Zbl 1411.34030
Llibre, Jaume; Zhang, Xiang
2018
Averaging theory of arbitrary order for piecewise smooth differential systems and its application. Zbl 1387.34069
Wei, Lijun; Zhang, Xiang
2018
Stability loss delay and smoothness of the return map in slow-fast systems. Zbl 1396.34042
Wang, Cheng; Zhang, Xiang
2018
Quadratic differential systems with complex conjugate invariant lines meeting at a finite point. Zbl 1393.37023
Schlomiuk, Dana; Zhang, Xiang
2018
On natural modes in moonpools and gaps in finite depth. Zbl 1419.76346
Molin, Bernard; Zhang, X.; Huang, H.; Remy, F.
2018
Dynamics of a nonlinear equation modelling the capillary rise. Zbl 1415.34062
Zhang, Xiang
2018
Integrability of dynamical systems: algebra and analysis. Zbl 1373.37053
Zhang, Xiang
2017
Sparse and scalable eigenstrain-based reduced order homogenization models for polycrystal plasticity. Zbl 1439.74328
Zhang, Xiang; Oskay, Caglar
2017
A note on local integrability of differential systems. Zbl 1385.34004
Zhang, Xiang
2017
Generalized involutive symmetry and its application in integrability of differential systems. Zbl 1383.34056
Wei, Lijun; Romanovski, Valery; Zhang, Xiang
2017
Limit cycles of the classical Liénard differential systems: a survey on the Lins Neto, de Melo and Pugh’s conjecture. Zbl 1381.34049
Llibre, Jaume; Zhang, Xiang
2017
Dynamics of some three-dimensional Lotka-Volterra systems. Zbl 1376.34030
Llibre, Jaume; Zhang, Xiang
2017
Equivalence of the Melnikov function method and the averaging method. Zbl 1377.34056
Han, Maoan; Romanovski, Valery G.; Zhang, Xiang
2016
Averaging methods of arbitrary order, periodic solutions and integrability. Zbl 1336.34062
Giné, Jaume; Llibre, Jaume; Wu, Kesheng; Zhang, Xiang
2016
Liouvillian integrability of polynomial differential systems. Zbl 1331.34006
Zhang, Xiang
2016
Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems. Zbl 1334.37051
Wei, Lijun; Zhang, Xiang
2016
A system of generalized Sylvester quaternion matrix equations and its applications. Zbl 1410.15037
Zhang, Xiang
2016
The number of polynomial solutions of polynomial Riccati equations. Zbl 1359.34020
Gasull, Armengol; Torregrosa, Joan; Zhang, Xiang
2016
Varieties and analytic normalizations of partially integrable systems. Zbl 1357.34072
Du, Zengji; Romanovski, Valery G.; Zhang, Xiang
2016
Normal form and limit cycle bifurcation of piecewise smooth differential systems with a center. Zbl 1344.34029
Wei, Lijun; Zhang, Xiang
2016
Liouvillian integrability versus Darboux polynomials. Zbl 1364.34016
Llibre, Jaume; Valls, Claudia; Zhang, Xiang
2016
Integrability of vector fields versus inverse Jacobian multipliers and normalizers. Zbl 1373.34003
Weng, Shiliang; Zhang, Xiang
2016
Center of planar quintic quasi-homogeneous polynomial differential systems. Zbl 1327.34054
Tang, Yilei; Wang, Long; Zhang, Xiang
2015
Vector fields with homogeneous nonlinearities and many limit cycles. Zbl 1326.34060
Gasull, Armengol; Yu, Jiang; Zhang, Xiang
2015
Eigenstrain based reduced order homogenization for polycrystalline materials. Zbl 1423.74796
Zhang, Xiang; Oskay, Caglar
2015
Improved coupling of finite element method with material point method based on a particle-to-surface contact algorithm. Zbl 1423.74870
Chen, Z. P.; Qiu, X. M.; Zhang, X.; Lian, Y. P.
2015
On polynomial integrability of the Euler equations on $$\mathfrak{so}(4)$$. Zbl 1325.34003
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
2015
The completely integrable differential systems are essentially linear differential systems. Zbl 1332.34004
Llibre, Jaume; Valls, Claudia; Zhang, Xiang
2015
A mesh-grading material point method and its parallelization for problems with localized extreme deformation. Zbl 1423.74901
Lian, Y. P.; Yang, P. F.; Zhang, X.; Zhang, F.; Liu, Y.; Huang, P.
2015
On the limit cycles of linear differential systems with homogeneous nonlinearities. Zbl 1337.34034
Llibre, Jaume; Zhang, Xiang
2015
Varieties of local integrability of analytic differential systems and their applications. Zbl 1305.34022
Romanovski, Valery G.; Xia, Yonghui; Zhang, Xiang
2014
Nonuniform dichotomy spectrum and normal forms for nonautonomous differential systems. Zbl 1306.34083
Zhang, Xiang
2014
Local Darboux first integrals of analytic differential systems. Zbl 1291.34068
Llibre, Jaume; Walcher, Sebastian; Zhang, Xiang
2014
On the analytic integrability of the 5-dimensional Lorenz system for the gravity-wave activity. Zbl 1287.34003
Llibre, Jaume; Saghin, Radu; Zhang, Xiang
2014
On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities. Zbl 1296.34076
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
2014
Analytic normalization of analytically integrable differential systems near a periodic orbit. Zbl 1297.34055
Wu, Kesheng; Zhang, Xiang
2014
Global $${C}^{\infty}$$ integrability of cubic-linear polynomial differential systems. Zbl 1319.34009
Pan, Yangyou; Wang, Cong; Zhang, Xiang
2014
Darboux integrability and algebraic limit cycles for a class of polynomial differential systems. Zbl 1308.34040
Cao, Jinlong; Llibre, Jaume; Zhang, Xiang
2014
Inverse Jacobian multipliers and Hopf bifurcation on center manifolds. Zbl 1417.34089
Zhang, Xiang
2014
Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems. Zbl 1301.34055
Liang, Feng; Han, Maoan; Zhang, Xiang
2013
The sliding bifurcations in planar piecewise smooth differential systems. Zbl 1290.34047
Pi, Dingheng; Zhang, Xiang
2013
Analytic integrable systems: analytic normalization and embedding flows. Zbl 1335.34072
Zhang, Xiang
2013
Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces. Zbl 1338.37038
Wu, Kesheng; Zhang, Xiang
2013
On the sliding bifurcation of a class of planar Filippov systems. Zbl 1270.34088
Pi, Dingheng; Yu, Jiang; Zhang, Xiang
2013
Study of a transition in the qualitative behavior of a simple oscillator with Coulomb friction. Zbl 1279.34064
Pratt, Elaine; Léger, Alain; Zhang, Xiang
2013
Comment on “On the polynomial integrability of the Kirchhoff equations”. Zbl 1267.34005
Zhang, Xiang
2013
Algebraic aspects of integrability for polynomial differential systems. Zbl 1295.34001
Pan, Yangyou; Zhang, Xiang
2013
On the Darboux integrability of polynomial differential systems. Zbl 1266.34002
Llibre, Jaume; Zhang, Xiang
2012
Darboux polynomials and rational first integrals of the generalized Lorenz systems. Zbl 1246.34018
Wu, Kesheng; Zhang, Xiang
2012
On the Hopf-zero bifurcation of the Michelson system. Zbl 1220.34070
Llibre, Jaume; Zhang, Xiang
2011
The 16th Hilbert problem on algebraic limit cycles. Zbl 1365.34064
Zhang, Xiang
2011
Global structure of quaternion polynomial differential equations. Zbl 1251.34019
Zhang, Xiang
2011
Generalized rational first integrals of analytic differential systems. Zbl 1232.34004
Cong, Wang; Llibre, Jaume; Zhang, Xiang
2011
The hyperelliptic limit cycles of the Liénard systems. Zbl 1208.34038
Yu, Xiaolan; Zhang, Xiang
2011
The embedding flows of $$C^\infty$$ hyperbolic diffeomorphisms. Zbl 1221.37101
Zhang, Xiang
2011
Rational first integrals in the Darboux theory of integrability in $$\mathbb C^n$$. Zbl 1190.34003
Llibre, Jaume; Zhang, Xiang
2010
Embedding smooth diffeomorphisms in flows. Zbl 1194.37074
Zhang, Xiang
2010
Input/output selection in DEA under expert information, with application to financial markets. Zbl 1206.91019
Edirisinghe, N. C. P.; Zhang, X.
2010
Limit cycles for a class of third-order differential equations. Zbl 1196.37087
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
2010
Integrable natural Hamiltonian systems on the suspensions of toric automorphism. Zbl 1202.37019
Liu, Fei; Zhang, Xiang
2010
Darboux theory of integrability in $$\mathbb C^n$$ taking into account the multiplicity. Zbl 1163.34003
Llibre, Jaume; Zhang, Xiang
2009
Darboux theory of integrability for polynomial vector fields in taking into account the multiplicity at infinity. Zbl 1198.34054
Llibre, Jaume; Zhang, Xiang
2009
Hopf bifurcation in higher dimensional differential systems via the averaging method. Zbl 1171.34027
Llibre, Jaume; Zhang, Xiang
2009
One-dimensional quaternion homogeneous polynomial differential equations. Zbl 1223.34060
Gasull, Armengol; Llibre, Jaume; Zhang, Xiang
2009
Embedding diffeomorphisms in flows in Banach spaces. Zbl 1177.37026
Zhang, Xiang
2009
Limit cycles of differential systems via the averaging methods. Zbl 1362.34066
Pi, Dingheng; Zhang, Xiang
2009
Integrable Hamiltonian systems with positive topological entropy. Zbl 1194.34015
Liu, Fei; Chen, Cheng; Zhang, Xiang
2009
Analytic normalization of analytic integrable systems and the embedding flows. Zbl 1141.34004
Zhang, Xiang
2008
First integrals and normal forms for germs of analytic vector fields. Zbl 1166.34018
Chen, Jian; Yi, Yingfei; Zhang, Xiang
2008
On the algebraic limit cycles of Liénard systems. Zbl 1158.34021
Llibre, Jaume; Zhang, Xiang
2008
The topological structure of the Rabinovich system having an invariant algebraic surface. Zbl 1141.34028
Chen, Cheng; Cao, Jinlong; Zhang, Xiang
2008
The Chen system having an invariant algebraic surface. Zbl 1165.34357
Cao, Jinlong; Chen, Cheng; Zhang, Xiang
2008
Portfolio selection under DEA-based relative financial strength indicators: Case of US industries. Zbl 1153.90454
Edirisinghe, N. C. P.; Zhang, X.
2008
Limit cycles coming from the perturbation of 2-dimensional centers of vector fields in $$\mathbb R^3$$. Zbl 1202.37072
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
2008
Darboux polynomials and algebraic integrability of the Chen system. Zbl 1148.34001
Lü, Tinghua; Zhang, Xiang
2007
Dynamics of the Lorenz system having an invariant algebraic surface. Zbl 1152.81361
Cao, Jinlong; Zhang, Xiang
2007
Orthogonal separable Hamiltonian systems on $$T^{2}$$. Zbl 1136.37031
Chen, Cheng; Liu, Fei; Zhang, Xiang
2007
Melnikov functions for period annulus, nondegenerate centers, heteroclinic and homoclinic cycles. Zbl 1052.37015
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2004
Exponential factors and Darboux integrability for the Rössler system. Zbl 1085.34505
Zhang, Xiang
2004
...and 37 more Documents
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### Cited by 594 Authors

 172 Llibre, Jaume 80 Valls Anglés, Cláudia 68 Zhang, Xiang 43 Han, Maoan 23 Giné, Jaume 20 Algaba, Antonio 15 Pantazi, Chara 13 Romanovski, Valery G. 11 Ferragut, Antoni 11 Shi, Shaoyun 11 Xia, Yonghui 10 García, Cristóbal 10 García, Isaac A. 10 Merino, Manuel 10 Messias, Marcelo 10 Rodríguez-Luis, Alejandro J. 10 Xiong, Yanqin 9 Huang, Jianfeng 9 Li, Shimin 9 Liang, Haihua 9 Oliveira, Regilene D. S. 9 Zhao, Liqin 8 Gasull, Armengol 8 Liu, Changjian 8 Walcher, Sebastian 8 Wei, Zhouchao 8 Yang, Junmin 8 Yu, Jiang 7 Demina, Maria V. 7 Fernández-Sánchez, Fernando 7 Huang, Chengdai 7 Wei, Lijun 7 Yang, Jiazhong 6 Li, Tao 6 Ma, Changfeng 6 Novaes, Douglas Duarte 6 Ramírez, Rafael O. 6 Wang, Lei 6 Yang, Jihua 6 Yang, Xiaosong 6 Zhao, Yulin 5 Buzzi, Claudio Aguinaldo 5 Cao, Jinlong 5 Chèze, Guillaume 5 Christopher, Colin J. 5 García, Belén 5 Giacomini, Hector J. 5 Hu, Zhaoping 5 Huang, Kaiyin 5 Li, Weigu 5 Li, Wenlei 5 Liang, Feng 5 Pérez del Río, Jesús S. 5 Reyes, Manuel 5 Sadovskaia, Natalia 5 Sheng, Lijuan 5 Tang, Yilei 5 Tian, Yuzhou 5 Xu, Zhiguo 4 Aziz, Waleed 4 Bai, Yuzhen 4 Benterki, Rebiha 4 Cao, Jinde 4 Chen, Hebai 4 Chen, Xingwu 4 Huang, Lihong 4 Lăzureanu, Cristian 4 Li, Chengliang 4 Li, Feng 4 Li, Jibin 4 Pi, Dingheng 4 Reinol, Alisson C. 4 Teixeira, Marco Antonio 4 Torregrosa, Joan 4 Vulpe, Nicolae I. 4 Wang, Jiafu 4 Wu, Hao 4 Xiao, Min 4 Yu, Pei 3 Bolaños, Yudy 3 Buică, Adriana 3 Chavarriga, Javier 3 Chen, Aiyong 3 Corrêa Barros, Maurício Jun. 3 Da Silva, Paulo Ricardo 3 Du, Zhengdong 3 Freire Macías, Emilio 3 Gamero, Estanislao 3 Hu, Yanxia 3 Huan, Songmei 3 Huang, Bo 3 Kruff, Niclas 3 Li, Xianyi 3 Li, Xinli 3 Liu, Shanshan 3 Liu, Yongjian 3 Lombardero, Antón 3 Mahdi, Adam 3 Makhlouf, Ammar 3 Maza, Susanna ...and 494 more Authors
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### Cited in 125 Serials

 94 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 69 Journal of Differential Equations 47 Qualitative Theory of Dynamical Systems 41 Journal of Mathematical Analysis and Applications 23 Bulletin des Sciences Mathématiques 17 Journal of Mathematical Physics 17 Nonlinear Dynamics 15 Chaos, Solitons and Fractals 14 Discrete and Continuous Dynamical Systems. Series B 14 Journal of Applied Analysis and Computation 13 Applied Mathematics and Computation 13 Journal of Dynamics and Differential Equations 13 Nonlinear Analysis. Real World Applications 12 Advances in Difference Equations 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 Discrete and Continuous Dynamical Systems 10 Applied Mathematics Letters 9 Physica D 9 Acta Mathematica Sinica. English Series 8 Journal of Geometry and Physics 8 Dynamical Systems 7 Rendiconti del Circolo Matemàtico di Palermo. Serie II 7 Communications in Nonlinear Science and Numerical Simulation 6 Journal of Nonlinear Mathematical Physics 5 Rocky Mountain Journal of Mathematics 5 Journal of Computational and Applied Mathematics 5 Proceedings of the American Mathematical Society 5 Chaos 5 Nonlinear Analysis. Hybrid Systems 3 Computers & Mathematics with Applications 3 Physics Letters. A 3 Acta Applicandae Mathematicae 3 Journal of Symbolic Computation 3 Mathematical Problems in Engineering 3 Mathematical Physics, Analysis and Geometry 3 Regular and Chaotic Dynamics 3 Journal of Dynamical and Control Systems 3 Communications in Contemporary Mathematics 3 Journal of Systems Science and Complexity 3 Communications on Pure and Applied Analysis 3 International Journal of Geometric Methods in Modern Physics 3 Mediterranean Journal of Mathematics 3 Advances in Mathematical Physics 3 Science China. Mathematics 3 Journal of Function Spaces 2 Journal of Pure and Applied Algebra 2 Mathematische Zeitschrift 2 Ergodic Theory and Dynamical Systems 2 European Journal of Applied Mathematics 2 Expositiones Mathematicae 2 Electronic Journal of Differential Equations (EJDE) 2 NoDEA. Nonlinear Differential Equations and Applications 2 Journal of Difference Equations and Applications 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 2 Advanced Nonlinear Studies 2 SIAM Journal on Applied Dynamical Systems 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Journal of Siberian Federal University. Mathematics & Physics 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Classical and Quantum Gravity 1 Computers and Fluids 1 Communications in Mathematical Physics 1 Journal of the Franklin Institute 1 Mathematical Methods in the Applied Sciences 1 Physica A 1 Reports on Mathematical Physics 1 Theoretical and Mathematical Physics 1 Mathematics of Computation 1 Advances in Mathematics 1 Canadian Journal of Mathematics 1 Geometriae Dedicata 1 Journal of Functional Analysis 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Transactions of the American Mathematical Society 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Complexity 1 Revista Matemática Iberoamericana 1 Mathematical and Computer Modelling 1 Neural Networks 1 The Journal of Geometric Analysis 1 Applications of Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Communications in Statistics. Theory and Methods 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Nonlinear Science 1 Tatra Mountains Mathematical Publications 1 Topological Methods in Nonlinear Analysis 1 Computational and Applied Mathematics 1 Turkish Journal of Mathematics 1 Advances in Applied Clifford Algebras 1 Journal of Lie Theory 1 Buletinul Academiei de Științe a Republicii Moldova. Matematica 1 Integral Transforms and Special Functions 1 The Ramanujan Journal 1 Differential Equations and Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Abstract and Applied Analysis ...and 25 more Serials
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### Cited in 40 Fields

 566 Ordinary differential equations (34-XX) 243 Dynamical systems and ergodic theory (37-XX) 29 Mechanics of particles and systems (70-XX) 26 Biology and other natural sciences (92-XX) 18 Partial differential equations (35-XX) 11 Systems theory; control (93-XX) 10 Numerical analysis (65-XX) 9 Difference and functional equations (39-XX) 6 Operator theory (47-XX) 6 Computer science (68-XX) 6 Relativity and gravitational theory (83-XX) 5 Field theory and polynomials (12-XX) 5 Algebraic geometry (14-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Geophysics (86-XX) 4 Commutative algebra (13-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Special functions (33-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Number theory (11-XX) 3 Nonassociative rings and algebras (17-XX) 3 Group theory and generalizations (20-XX) 3 Functions of a complex variable (30-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Optics, electromagnetic theory (78-XX) 2 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Probability theory and stochastic processes (60-XX) 2 Fluid mechanics (76-XX) 2 Astronomy and astrophysics (85-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Topological groups, Lie groups (22-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)