# zbMATH — the first resource for mathematics

## Zhang, Xiang

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 Author ID: zhang.xiang Published as: Zhang, X.; Zhang, Xiang Homepage: http://math.sjtu.edu.cn/faculty/zhangxiang/Homepage%20English.html External Links: ORCID · ResearchGate
 Documents Indexed: 176 Publications since 1990, including 2 Books Reviewing Activity: 27 Reviews
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#### Co-Authors

 44 single-authored 44 Llibre, Jaume 6 Yu, Jiang 5 Li, Weigu 5 Wei, Lijun 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 Pi, Dingheng 2 Liu, Fei 2 Liu, Fei 2 Tang, Yilei 2 Torregrosa, Joan 2 Valls Anglés, Cláudia 2 Weng, Shiliang 2 Xu, Yuxing 2 Yi, Yingfei 1 Bai, Yuzhen 1 Chen, Jian 1 Christopher, Colin J. 1 Cong, Wang 1 Du, Zengji 1 Giné, Jaume 1 Léger, Alain 1 Liang, Feng 1 Lü, Tinghua 1 Mo, Jiaqi 1 Nicolau, Marcel 1 Pantazi, Chara 1 Ponce, Enrique 1 Pratt, Elaine 1 Saghin, Radu 1 Sheng, Lijuan 1 Walcher, Sebastian 1 Wang, Cong 1 Wang, Long 1 Wu, Qinkuan 1 Xia, Yonghui 1 Xie, Feng 1 Ye, Yanqian 1 Yu, Pei 1 Yu, Xiaolan 1 Zhang, Yuanfan
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#### Serials

 20 Journal of Differential Equations 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Nonlinearity 6 Journal of Physics A: Mathematical and General 6 Bulletin des Sciences Mathématiques 5 Qualitative Theory of Dynamical Systems 4 Journal of Mathematical Physics 4 Applied Mathematics and Mechanics. (English Edition) 4 Discrete and Continuous Dynamical Systems 3 Journal of Mathematical Analysis and Applications 3 Proceedings of the American Mathematical Society 3 Annals of Differential Equations 3 Mathematica Applicata 3 Journal of Dynamics and Differential Equations 2 Rocky Mountain Journal of Mathematics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 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 Physica D 2 Science in China. Series A 2 Journal of Anhui Normal University. Natural Science 2 Acta Mathematica Scientia. Series A. (Chinese Edition) 2 Nonlinear Analysis. Real World Applications 1 Communications in Mathematical Physics 1 Houston Journal of Mathematics 1 Journal of Geometry and Physics 1 American Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Journal of Functional Analysis 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 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 Journal of Jiangxi Normal University. Natural Science Edition 1 Systems Science and Mathematical Sciences 1 Dynamic Systems and Applications 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Expositiones Mathematicae 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 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 Journal of Systems Science and Complexity 1 Mediterranean Journal of Mathematics 1 Developments in Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Science China. Mathematics 1 Journal of Applied Analysis and Computation 1 Journal of Shanghai Normal University. Natural Sciences
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#### Fields

 121 Ordinary differential equations (34-XX) 50 Dynamical systems and ergodic theory (37-XX) 8 Partial differential equations (35-XX) 4 Integral equations (45-XX) 3 Mechanics of particles and systems (70-XX) 2 Differential geometry (53-XX) 2 Biology and other natural sciences (92-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH

117 Publications have been cited 957 times in 584 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
Polynomial first integrals for quasi-homogeneous polynomials differential systems. Zbl 1024.34001
Llibre, Jaume; Zhang, Xiang
2002
Invariant algebraic surfaces of the Lorenz system. Zbl 1059.34005
Llibre, Jaume; Zhang, Xiang
2002
Analytic normalization of analytic integrable systems and the embedding flows. Zbl 1141.34004
Zhang, Xiang
2008
Darboux theory of integrability for polynomial vector fields in taking into account the multiplicity at infinity. Zbl 1198.34054
Llibre, Jaume; Zhang, Xiang
2009
Rational first integrals in the Darboux theory of integrability in $$\mathbb C^n$$. Zbl 1190.34003
Llibre, Jaume; Zhang, Xiang
2010
Local first integrals of differential systems and diffeomorphisms. Zbl 1043.37010
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2003
Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems. Zbl 1301.34055
Liang, Feng; Han, Maoan; Zhang, Xiang
2013
Invariant algebraic surfaces of the Rikitake system. Zbl 0967.34002
Llibre, Jaume; Zhang, Xiang
2000
On the Darboux integrability of polynomial differential systems. Zbl 1266.34002
Llibre, Jaume; Zhang, Xiang
2012
Equivalence of the Melnikov function method and the averaging method. Zbl 1377.34056
Han, Maoan; Romanovski, Valery G.; Zhang, Xiang
2016
Darboux polynomials and algebraic integrability of the Chen system. Zbl 1148.34001
Lü, Tinghua; Zhang, Xiang
2007
Darboux integrability and invariant algebraic curves for planar polynomial systems. Zbl 1012.34035
Christopher, Colin; Llibre, Jaume; Pantazi, Chara; 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
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
On the differentiability of first integrals of two dimensional flows. Zbl 1010.34023
Li, Weigu; Llibre, Jaume; Nicolau, Marcel; Zhang, Xiang
2002
Darboux polynomials and rational first integrals of the generalized Lorenz systems. Zbl 1246.34018
Wu, Kesheng; Zhang, Xiang
2012
First integrals and normal forms for germs of analytic vector fields. Zbl 1166.34018
Chen, Jian; Yi, Yingfei; Zhang, Xiang
2008
Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces. Zbl 1194.34050
Zhang, Xiang; Llibre, Jaume
2002
On the number of limit cycles for some perturbed Hamiltonian polynomial systems. Zbl 0992.34021
Llibre, Jaume; Zhang, Xiang
2001
Averaging methods of arbitrary order, periodic solutions and integrability. Zbl 1336.34062
Giné, Jaume; Llibre, Jaume; Wu, Kesheng; Zhang, Xiang
2016
The sliding bifurcations in planar piecewise smooth differential systems. Zbl 1290.34047
Pi, Dingheng; Zhang, Xiang
2013
On the Hopf-zero bifurcation of the Michelson system. Zbl 1220.34070
Llibre, Jaume; Zhang, Xiang
2011
Varieties of local integrability of analytic differential systems and their applications. Zbl 1305.34022
Romanovski, Valery G.; Xia, Yonghui; Zhang, Xiang
2014
The 16th Hilbert problem on algebraic limit cycles. Zbl 1365.34064
Zhang, Xiang
2011
Dynamics of the Lorenz system having an invariant algebraic surface. Zbl 1152.81361
Cao, Jinlong; Zhang, Xiang
2007
Darboux integrability for the Rössler system. Zbl 1047.34002
Llibre, Jaume; Zhang, Xiang
2002
Integrability of dynamical systems: algebra and analysis. Zbl 1373.37053
Zhang, Xiang
2017
Center of planar quintic quasi-homogeneous polynomial differential systems. Zbl 1327.34054
Tang, Yilei; Wang, Long; Zhang, Xiang
2015
Local first integrals for systems of differential equations. Zbl 1055.34074
Zhang, Xiang
2003
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
A system of generalized Sylvester quaternion matrix equations and its applications. Zbl 1410.15037
Zhang, Xiang
2016
Liouvillian integrability of polynomial differential systems. Zbl 1331.34006
Zhang, Xiang
2016
Melnikov functions for period annulus, nondegenerate centers, heteroclinic and homoclinic cycles. Zbl 1052.37015
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2004
Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems. Zbl 1334.37051
Wei, Lijun; Zhang, Xiang
2016
Global structure of quaternion polynomial differential equations. Zbl 1251.34019
Zhang, Xiang
2011
Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces. Zbl 1338.37038
Wu, Kesheng; Zhang, Xiang
2013
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
Planar analytic vector fields with generalized rational first integrals. Zbl 1032.34029
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2001
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
One-dimensional quaternion homogeneous polynomial differential equations. Zbl 1223.34060
Gasull, Armengol; Llibre, Jaume; Zhang, Xiang
2009
On the algebraic limit cycles of Liénard systems. Zbl 1158.34021
Llibre, Jaume; Zhang, Xiang
2008
Exponential factors and Darboux integrability for the Rössler system. Zbl 1085.34505
Zhang, Xiang
2004
Invariant algebraic surfaces of the Rabinovich system. Zbl 1066.34027
Xie, Feng; Zhang, Xiang
2003
Exponential factors and Darbouxian first integrals of the Lorenz system. Zbl 1060.34004
Zhang, Xiang
2002
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
Stability loss delay and smoothness of the return map in slow-fast systems. Zbl 1396.34042
Wang, Cheng; Zhang, Xiang
2018
Eigenstrain based reduced order homogenization for polycrystalline materials. Zbl 1423.74796
Zhang, Xiang; Oskay, Caglar
2015
Vector fields with homogeneous nonlinearities and many limit cycles. Zbl 1326.34060
Gasull, Armengol; Yu, Jiang; Zhang, Xiang
2015
Local Darboux first integrals of analytic differential systems. Zbl 1291.34068
Llibre, Jaume; Walcher, Sebastian; Zhang, Xiang
2014
On the sliding bifurcation of a class of planar Filippov systems. Zbl 1270.34088
Pi, Dingheng; Yu, Jiang; Zhang, Xiang
2013
The Chen system having an invariant algebraic surface. Zbl 1165.34357
Cao, Jinlong; Chen, Cheng; 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
Invariant algebraic curves and rational first integrals of holomorphic foliations in $$\mathbb C P(2)$$. Zbl 1217.37049
Zhang, Xiang
2003
Polynomial first integrals of quadratic systems. Zbl 1041.34018
Llibre, Jaume; Zhang, Xiang
2001
Existence of limit cycles in a multiply-connected region. Zbl 0934.34023
Zhang, Xiang
1999
The completely integrable differential systems are essentially linear differential systems. Zbl 1332.34004
Llibre, Jaume; Valls, Claudia; Zhang, Xiang
2015
Nonuniform dichotomy spectrum and normal forms for nonautonomous differential systems. Zbl 1306.34083
Zhang, Xiang
2014
Portfolio selection under DEA-based relative financial strength indicators: Case of US industries. Zbl 1153.90454
Edirisinghe, N. C. P.; Zhang, X.
2008
Integrals of motion of the Rabinovich system. Zbl 0962.34034
Zhang, Xiang
2000
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
Varieties and analytic normalizations of partially integrable systems. Zbl 1357.34072
Du, Zengji; Romanovski, Valery G.; Zhang, Xiang
2016
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
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
Embedding diffeomorphisms in flows in Banach spaces. Zbl 1177.37026
Zhang, Xiang
2009
Relaxation oscillations in a slow-fast modified Leslie-Gower model. Zbl 1433.34069
Wang, Cheng; Zhang, Xiang
2019
Averaging theory of arbitrary order for piecewise smooth differential systems and its application. Zbl 1387.34069
Wei, Lijun; Zhang, Xiang
2018
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
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 polynomial integrability of the Euler equations on $$\mathfrak{so}(4)$$. Zbl 1325.34003
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
2015
Analytic normalization of analytically integrable differential systems near a periodic orbit. Zbl 1297.34055
Wu, Kesheng; Zhang, Xiang
2014
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
Dynamics of a nonlinear equation modelling the capillary rise. Zbl 1415.34062
Zhang, Xiang
2018
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
Liouvillian integrability versus Darboux polynomials. Zbl 1364.34016
Llibre, Jaume; Valls, Claudia; Zhang, Xiang
2016
On the limit cycles of linear differential systems with homogeneous nonlinearities. Zbl 1337.34034
Llibre, Jaume; Zhang, Xiang
2015
Darboux integrability and algebraic limit cycles for a class of polynomial differential systems. Zbl 1308.34040
Cao, Jinlong; Llibre, Jaume; Zhang, Xiang
2014
Global $${C}^{\infty}$$ integrability of cubic-linear polynomial differential systems. Zbl 1319.34009
Pan, Yangyou; Wang, Cong; Zhang, Xiang
2014
Input/output selection in DEA under expert information, with application to financial markets. Zbl 1206.91019
Edirisinghe, N. C. P.; Zhang, X.
2010
Integrable Hamiltonian systems with positive topological entropy. Zbl 1194.34015
Liu, Fei; Chen, Cheng; Zhang, Xiang
2009
Orthogonal separable Hamiltonian systems on $$T^{2}$$. Zbl 1136.37031
Chen, Cheng; Liu, Fei; Zhang, Xiang
2007
Planar analytic systems having locally analytic first integrals at an isolated singular point. Zbl 1056.34047
Zhang, Xiang
2004
Invariant hyperplanes and Darboux integrability of polynomial vector fields. Zbl 1054.34062
Zhang, Xiang
2002
Invariant algebraic surfaces of the Belousov-Zhabotinskii systems. Zbl 1127.34328
Llibre, Jaume; Zhang, Xiang
2001
Ergodicity of limit cycles in quadratic systems. Zbl 0979.34025
Zhang, Xiang
2001
Determination of the sign of divergence of a quadratic system at critical points. Zbl 0911.34024
Zhang, Xiang
1997
Uniqueness of limit cycles of quadratic system (III)$$_{m=0}$$. Zbl 0883.34036
Zhang, Xiang; Ye, Qin
1997
Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift. Zbl 07285692
Menozzi, S.; Pesce, A.; Zhang, X.
2021
The period function of Hamiltonian systems with separable variables. Zbl 07201505
Villadelprat, Jordi; Zhang, Xiang
2020
Constructing likelihood functions for interval-valued random variables. Zbl 1444.62139
Zhang, X.; Beranger, B.; Sisson, S. A.
2020
The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems. Zbl 1430.34039
Llibre, Jaume; Zhang, Xiang
2019
On natural modes in moonpools and gaps in finite depth. Zbl 1419.76346
Molin, Bernard; Zhang, X.; Huang, H.; Remy, F.
2018
Quadratic differential systems with complex conjugate invariant lines meeting at a finite point. Zbl 1393.37023
Schlomiuk, Dana; Zhang, Xiang
2018
Dynamics of some three-dimensional Lotka-Volterra systems. Zbl 1376.34030
Llibre, Jaume; Zhang, Xiang
2017
A note on local integrability of differential systems. Zbl 1385.34004
Zhang, Xiang
2017
Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift. Zbl 07285692
Menozzi, S.; Pesce, A.; Zhang, X.
2021
The period function of Hamiltonian systems with separable variables. Zbl 07201505
Villadelprat, Jordi; Zhang, Xiang
2020
Constructing likelihood functions for interval-valued random variables. Zbl 1444.62139
Zhang, X.; Beranger, B.; Sisson, S. A.
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
Relaxation oscillations in a slow-fast modified Leslie-Gower model. Zbl 1433.34069
Wang, Cheng; 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
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
Stability loss delay and smoothness of the return map in slow-fast systems. Zbl 1396.34042
Wang, Cheng; Zhang, Xiang
2018
Averaging theory of arbitrary order for piecewise smooth differential systems and its application. Zbl 1387.34069
Wei, Lijun; Zhang, Xiang
2018
Dynamics of a nonlinear equation modelling the capillary rise. Zbl 1415.34062
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
Quadratic differential systems with complex conjugate invariant lines meeting at a finite point. Zbl 1393.37023
Schlomiuk, Dana; Zhang, Xiang
2018
Integrability of dynamical systems: algebra and analysis. Zbl 1373.37053
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
A note on local integrability of differential systems. Zbl 1385.34004
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
A system of generalized Sylvester quaternion matrix equations and its applications. Zbl 1410.15037
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
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
Liouvillian integrability versus Darboux polynomials. Zbl 1364.34016
Llibre, Jaume; Valls, Claudia; 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
Center of planar quintic quasi-homogeneous polynomial differential systems. Zbl 1327.34054
Tang, Yilei; Wang, Long; Zhang, Xiang
2015
Eigenstrain based reduced order homogenization for polycrystalline materials. Zbl 1423.74796
Zhang, Xiang; Oskay, Caglar
2015
Vector fields with homogeneous nonlinearities and many limit cycles. Zbl 1326.34060
Gasull, Armengol; 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
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
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 polynomial integrability of the Euler equations on $$\mathfrak{so}(4)$$. Zbl 1325.34003
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
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
Local Darboux first integrals of analytic differential systems. Zbl 1291.34068
Llibre, Jaume; Walcher, Sebastian; Zhang, Xiang
2014
Nonuniform dichotomy spectrum and normal forms for nonautonomous differential systems. Zbl 1306.34083
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
Analytic normalization of analytically integrable differential systems near a periodic orbit. Zbl 1297.34055
Wu, Kesheng; 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
Global $${C}^{\infty}$$ integrability of cubic-linear polynomial differential systems. Zbl 1319.34009
Pan, Yangyou; Wang, Cong; 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
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
Analytic integrable systems: analytic normalization and embedding flows. Zbl 1335.34072
Zhang, Xiang
2013
The sliding bifurcations in planar piecewise smooth differential systems. Zbl 1290.34047
Pi, Dingheng; 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
Algebraic aspects of integrability for polynomial differential systems. Zbl 1295.34001
Pan, Yangyou; Zhang, Xiang
2013
Comment on “On the polynomial integrability of the Kirchhoff equations”. Zbl 1267.34005
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
Integrable natural Hamiltonian systems on the suspensions of toric automorphism. Zbl 1202.37019
Liu, Fei; Zhang, Xiang
2010
Limit cycles for a class of third-order differential equations. Zbl 1196.37087
Llibre, Jaume; Yu, Jiang; 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 Chen system having an invariant algebraic surface. Zbl 1165.34357
Cao, Jinlong; Chen, Cheng; 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
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
Planar analytic systems having locally analytic first integrals at an isolated singular point. Zbl 1056.34047
Zhang, Xiang
2004
Local first integrals of differential systems and diffeomorphisms. Zbl 1043.37010
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2003
Local first integrals for systems of differential equations. Zbl 1055.34074
Zhang, Xiang
2003
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
Invariant algebraic surfaces of the Rabinovich system. Zbl 1066.34027
Xie, Feng; Zhang, Xiang
2003
Invariant algebraic curves and rational first integrals of holomorphic foliations in $$\mathbb C P(2)$$. Zbl 1217.37049
Zhang, Xiang
2003
Polynomial first integrals for quasi-homogeneous polynomials differential systems. Zbl 1024.34001
Llibre, Jaume; Zhang, Xiang
2002
Invariant algebraic surfaces of the Lorenz system. Zbl 1059.34005
Llibre, Jaume; Zhang, Xiang
2002
Darboux integrability and invariant algebraic curves for planar polynomial systems. Zbl 1012.34035
Christopher, Colin; Llibre, Jaume; Pantazi, Chara; 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
On the differentiability of first integrals of two dimensional flows. Zbl 1010.34023
Li, Weigu; Llibre, Jaume; Nicolau, Marcel; Zhang, Xiang
2002
Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces. Zbl 1194.34050
Zhang, Xiang; Llibre, Jaume
2002
Darboux integrability for the Rössler system. Zbl 1047.34002
Llibre, Jaume; Zhang, Xiang
2002
Exponential factors and Darbouxian first integrals of the Lorenz system. Zbl 1060.34004
Zhang, Xiang
2002
Invariant hyperplanes and Darboux integrability of polynomial vector fields. Zbl 1054.34062
Zhang, Xiang
2002
On the number of limit cycles for some perturbed Hamiltonian polynomial systems. Zbl 0992.34021
Llibre, Jaume; Zhang, Xiang
2001
Planar analytic vector fields with generalized rational first integrals. Zbl 1032.34029
Li, Weigu; Llibre, Jaume; Zhang, Xiang
2001
...and 17 more Documents
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#### Cited by 596 Authors

 151 Llibre, Jaume 78 Valls Anglés, Cláudia 65 Zhang, Xiang 33 Han, Maoan 23 Giné, Jaume 16 Algaba, Antonio 13 Romanovski, Valery G. 11 Ferragut, Antoni 11 Pantazi, Chara 11 Shi, Shaoyun 10 Messias, Marcelo 9 García, Isaac A. 9 Rodríguez-Luis, Alejandro J. 8 Huang, Jianfeng 8 Li, Shimin 8 Merino, Manuel 8 Oliveira, Regilene D. S. 8 Wei, Zhouchao 8 Xia, Yonghui 8 Yang, Junmin 7 Fernández-Sánchez, Fernando 7 García, Cristóbal 7 Gasull, Armengol 7 Huang, Chengdai 7 Liang, Haihua 7 Zhao, Yulin 6 Liu, Changjian 6 Ramírez, Rafael O. 6 Walcher, Sebastian 6 Xiong, Yanqin 6 Yang, Jiazhong 6 Zhao, Liqin 5 Cao, Jinlong 5 Chèze, Guillaume 5 García, Belén 5 Giacomini, Hector J. 5 He, ZhuoHeng 5 Hu, Zhaoping 5 Huang, Kaiyin 5 Li, Weigu 5 Li, Wenlei 5 Liang, Feng 5 Pérez del Río, Jesús S. 5 Sadovskaia, Natalia 5 Sheng, Lijuan 5 Tang, Yilei 5 Wei, Lijun 5 Wu, Hao 5 Xu, Zhiguo 5 Yu, Jiang 5 Yu, Pei 4 Bai, Yuzhen 4 Buzzi, Claudio Aguinaldo 4 Cao, Jinde 4 Chen, Hebai 4 Christopher, Colin J. 4 Du, Zengji 4 Li, Chengliang 4 Li, Jibin 4 Ma, Changfeng 4 Novaes, Douglas Duarte 4 Reinol, Alisson C. 4 Reyes, Manuel 4 Vulpe, Nicolae I. 4 Xiao, Min 4 Yang, Jihua 4 Zangeneh, Hamid R. Z. 3 Bolaños, Yudy 3 Buică, Adriana 3 Chavarriga, Javier 3 Corrêa Barros, Maurício Jun. 3 Demina, Maria V. 3 Fernando Mello, Luis 3 Hu, Yanxia 3 Jiang, Jiao 3 Lăzureanu, Cristian 3 Li, Feng 3 Li, Xinli 3 Liu, Yongjian 3 Mahdi, Adam 3 Makhlouf, Ammar 3 Maza, Susanna 3 Medrado, João C. R. 3 Schlomiuk, Dana I. 3 Shafer, Douglas S. 3 Teixeira, Marco Antonio 3 Tudoran, Răzvan Micu 3 Wang, Lei 3 Wang, Zhengxin 3 Wu, Kesheng 3 Yang, Qigui 3 Yang, Xiaosong 3 Zhang, Weinian 2 Acosta Humánez, Primitivo Belén 2 Akram, Muhammad 2 Ali, Ilyas 2 Atabaigi, Ali 2 Augarde, Charles Edward 2 Barreira, Luis Manuel 2 Benterki, Rebiha ...and 496 more Authors
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#### Cited in 115 Serials

 77 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 62 Journal of Differential Equations 38 Journal of Mathematical Analysis and Applications 35 Qualitative Theory of Dynamical Systems 23 Bulletin des Sciences Mathématiques 17 Nonlinear Dynamics 15 Journal of Mathematical Physics 15 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Journal of Dynamics and Differential Equations 13 Nonlinear Analysis. Real World Applications 12 Applied Mathematics and Computation 12 Applied Mathematics Letters 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Chaos, Solitons and Fractals 10 Discrete and Continuous Dynamical Systems 10 Advances in Difference Equations 9 Computer Methods in Applied Mechanics and Engineering 9 Discrete and Continuous Dynamical Systems. Series B 8 Journal of Geometry and Physics 8 Acta Mathematica Sinica. English Series 7 Computers & Mathematics with Applications 6 Physica D 6 Mathematical Problems in Engineering 6 Journal of Nonlinear Mathematical Physics 6 Dynamical Systems 5 Rocky Mountain Journal of Mathematics 5 Journal of Computational and Applied Mathematics 5 Proceedings of the American Mathematical Society 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Communications in Nonlinear Science and Numerical Simulation 4 Advances in Applied Clifford Algebras 4 Chaos 3 Physics Letters. A 3 European Journal of Operational Research 3 Regular and Chaotic Dynamics 3 Journal of Systems Science and Complexity 3 International Journal of Geometric Methods in Modern Physics 3 Science China. Mathematics 3 Journal of Function Spaces 2 Ergodic Theory and Dynamical Systems 2 Acta Applicandae Mathematicae 2 Journal of Symbolic Computation 2 European Journal of Applied Mathematics 2 Electronic Journal of Differential Equations (EJDE) 2 NoDEA. Nonlinear Differential Equations and Applications 2 Abstract and Applied Analysis 2 Mathematical Physics, Analysis and Geometry 2 Communications in Contemporary Mathematics 2 Advanced Nonlinear Studies 2 SIAM Journal on Applied Dynamical Systems 2 Mediterranean Journal of Mathematics 2 Nonlinear Analysis. Hybrid Systems 2 Advances in Mathematical Physics 2 Journal of Applied Analysis and Computation 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Computers and Fluids 1 Communications in Mathematical Physics 1 Journal of Fluid Mechanics 1 Journal of the Franklin Institute 1 Mathematical Methods in the Applied Sciences 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 Journal of Pure and Applied Algebra 1 Mathematische Zeitschrift 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 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Applied Mathematical Modelling 1 Communications in Statistics. Theory and Methods 1 Journal of Nonlinear Science 1 Topological Methods in Nonlinear Analysis 1 Computational and Applied Mathematics 1 Turkish Journal of Mathematics 1 Integral Transforms and Special Functions 1 Complexity 1 Engineering Analysis with Boundary Elements 1 Journal of Difference Equations and Applications 1 Mathematics and Mechanics of Solids 1 Differential Equations and Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Journal of Inequalities and Applications 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 DGDS. Differential Geometry – Dynamical Systems 1 Differential Equations 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Foundations of Computational Mathematics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris ...and 15 more Serials
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#### Cited in 41 Fields

 472 Ordinary differential equations (34-XX) 202 Dynamical systems and ergodic theory (37-XX) 27 Mechanics of particles and systems (70-XX) 21 Partial differential equations (35-XX) 21 Biology and other natural sciences (92-XX) 16 Numerical analysis (65-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 12 Mechanics of deformable solids (74-XX) 10 Systems theory; control (93-XX) 7 Difference and functional equations (39-XX) 6 Geophysics (86-XX) 6 Operations research, mathematical programming (90-XX) 5 Field theory and polynomials (12-XX) 5 Algebraic geometry (14-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Computer science (68-XX) 5 Fluid mechanics (76-XX) 5 Relativity and gravitational theory (83-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Special functions (33-XX) 4 Operator theory (47-XX) 3 Number theory (11-XX) 3 Commutative algebra (13-XX) 3 Group theory and generalizations (20-XX) 3 Differential geometry (53-XX) 3 Statistics (62-XX) 2 Nonassociative rings and algebras (17-XX) 2 Integral equations (45-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Astronomy and astrophysics (85-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)