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Author ID: lin.xiaobiao Recent zbMATH articles by "Lin, Xiaobiao"
Published as: Lin, Xiao-Biao; Lin, Xiaobiao; Lin, X.-B.
Documents Indexed: 58 Publications since 1982
Co-Authors: 27 Co-Authors with 32 Joint Publications
1,005 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

47 Publications have been cited 619 times in 483 Documents Cited by Year
Using Melnikov’s method to solve Silnikov’s problems. Zbl 0714.34070
Lin, Xiao-Biao
77
1990
Smooth invariant foliations in infinite dimensional spaces. Zbl 0749.58043
Chow, Shui-Nee; Lin, Xiao-Biao; Lu, Kening
69
1991
Upper semicontinuity of attractors for approximations of semigroups and partial differential equations. Zbl 0666.35013
Hale, Jack K.; Lin, Xiao-Biao; Raugel, Geneviève
66
1988
Exponential dichotomies and homoclinic orbits in functional differential equations. Zbl 0589.34055
Lin, Xiaobiao
56
1986
Heteroclinic orbits for retarded functional differential equations. Zbl 0611.34074
Hale, Jack K.; Lin, X.-B.
53
1986
Traveling wave solutions for a predator-prey system with sigmoidal response function. Zbl 1252.34048
Lin, Xiaobiao; Weng, Peixuan; Wu, Chufen
42
2011
Bifurcation of a homoclinic orbit with a saddle-node equilibrium. Zbl 0727.58026
Chow, Shuinee; Lin, Xiaobiao
31
1990
Symbolic dynamics and nonlinear semiflows. Zbl 0632.58027
Hale, Jack K.; Lin, Xiao-Biao
25
1986
A shadowing lemma with applications to semilinear parabolic equations. Zbl 0696.34033
Chow, Shui-Nee; Lin, Xiao-Biao; Palmer, Kenneth J.
22
1989
Shadowing lemma and singularly perturbed boundary value problems. Zbl 0686.34059
Lin, Xiaobiao
20
1989
Transition layers for singularly perturbed delay differential equations with monotone nonlinearities. Zbl 0684.34071
Chow, Shui-Nee; Lin, Xiao-Biao; Mallet-Paret, John
16
1989
Heteroclinic bifurcation and singularly perturbed boundary value problems. Zbl 0708.34017
Lin, Xiao-Biao
15
1990
Exponential dichotomies in intermediate spaces with applications to a diffusively perturbed predator-prey model. Zbl 0806.35078
Lin, Xiaobiao
13
1994
Construction and asymptotic stability of structurally stable internal layer solutions. Zbl 0986.34043
Lin, Xiao-Biao
13
2001
Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws. Zbl 1056.35112
Lin, Xiao-Biao; Schecter, Stephen
10
2003
Multiple internal layer solutions generated by spatially oscillatory perturbations. Zbl 0978.35019
Hale, Jack K.; Lin, Xiao-Biao
7
1999
A multiplicity theorem for hyperbolic systems. Zbl 0679.34077
Neves, Aloisio Freiria; Lin, Xiaobiao
7
1988
Improved bicharacteristic schemes for two-dimensional elastodynamic equations. Zbl 0833.73073
Lin, X.; Ballman, J.
7
1995
Homoclinic bifurcations with weakly expanding center manifolds. Zbl 0873.34031
Lin, Xiao-Biao
6
1996
Shadowing matching errors for wave-front-like solutions. Zbl 0864.35010
Lin, Xiao-Biao
6
1996
Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain. Zbl 1096.65106
Lai, Ming-Chih; Li, Zhilin; Lin, Xiaobiao
6
2006
Examples of transverse homoclinic orbits in delay equations. Zbl 0613.34060
Hale, Jack K.; Lin, Xiao-Biao
6
1986
Local and global existence of multiple waves near formal approximations. Zbl 0855.35009
Lin, Xiao-Biao
5
1996
Multiple transverse homoclinic solutions near a degenerate homoclinic orbit. Zbl 1332.34081
Lin, Xiao-Biao; Long, Bin; Zhu, Changrong
5
2015
Algebraic dichotomies with an application to the stability of Riemann solutions of conservation laws. Zbl 1192.34064
Lin, Xiao-Biao
5
2009
Transonic evaporation waves in a spherically symmetric nozzle. Zbl 1307.35231
Lin, Xiaobiao; Wechselberger, Martin
5
2014
Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system. Zbl 0852.35012
Lin, Xiao-Biao
4
1996
Traveling wave solutions in coupled Chua’s circuits. I: Periodic solutions. Zbl 1307.34025
Chow, Shui-Nee; Jiang, Ming; Lin, Xiaobiao
4
2013
\(L^2\) semigroup and linear stability for Riemann solutions of conservation laws. Zbl 1113.35124
Lin, Xiaobiao
3
2005
Multistage evolutionary model for carcinogenesis mutations. Zbl 1014.92018
Ahangar, Reza; Lin, Xiao-Biao
3
2003
Standing waves for phase transitions in a spherically symmetric nozzle. Zbl 1242.76330
Fan, Haitao; Lin, Xiao-Biao
3
2012
Slow eigenvalues of self-similar solutions of the Dafermos regularization of a system of conservation laws: an analytic approach. Zbl 1098.35102
Lin, Xiao-Biao
2
2006
Analytic semigroup generated by the linearization of a Riemann-Dafermos solution. Zbl 1073.35160
Lin, Xiao-Biao
2
2004
A dynamical systems approach to traveling wave solutions for liquid/vapor phase transition. Zbl 1263.35061
Fan, Haitao; Lin, Xiao-Biao
2
2012
Stability of standing waves for monostable reaction-convection equations in a large bounded domain with boundary conditions. Zbl 1323.35090
Lin, Xiao-Biao
2
2013
Exponential dichotomy and stability of long periodic solutions in predator-prey models with diffusion. Zbl 0823.35098
Lin, X. B.
1
1992
Fatigue growth simulation for cracks in notched and unnotched round bars. Zbl 0899.73423
Lin, X. B.; Smith, R. A.
1
1998
Another brief proof of the Sylvester theorem. Zbl 0663.51008
Lin, X. B.
1
1988
Heteroclinic and periodic cycles in a perturbed convection model. Zbl 1013.34041
Lin, Xiao-Biao; Vivancos, Ignacio B.
1
2002
Generalized Rankine-Hugoniot condition and shock solutions for quasilinear hyperbolic systems. Zbl 0978.35032
Lin, Xiao-Biao
1
2000
Gearhart-Prüss theorem and linear stability for Riemann solutions of conservation laws. Zbl 1132.35010
Lin, Xiao-Biao
1
2007
Codiagonalization of matrices and existence of multiple homoclinic solutions. Zbl 1488.37037
Lin, Xiaobiao; Zhu, Changrong
1
2017
Collapsing and explosion waves in phase transitions with metastability, existence, stability and related Riemann problems. Zbl 1203.35061
Fan, Haitao; Lin, Xiao-Biao
1
2010
Stability of concatenated traveling waves: alternate approaches. Zbl 1353.35101
Lin, Xiao-Biao; Schecter, Stephen
1
2015
A shadowing lemma for maps in infinite dimensions. Zbl 0689.34041
Chow, Shui-Nee; Lin, Xiao-Biao; Palmer, Kenneth J.
1
1989
Bifurcation analysis on a coral-starfish model. Zbl 0721.34038
Antonelli, P. L.; Lin, X.
1
1990
Chaotic traveling wave solutions in coupled Chua’s circuits. Zbl 1423.34044
Geng, Fengjie; Lin, Xiao-Biao; Liu, Xingbo
1
2019
Chaotic traveling wave solutions in coupled Chua’s circuits. Zbl 1423.34044
Geng, Fengjie; Lin, Xiao-Biao; Liu, Xingbo
1
2019
Codiagonalization of matrices and existence of multiple homoclinic solutions. Zbl 1488.37037
Lin, Xiaobiao; Zhu, Changrong
1
2017
Multiple transverse homoclinic solutions near a degenerate homoclinic orbit. Zbl 1332.34081
Lin, Xiao-Biao; Long, Bin; Zhu, Changrong
5
2015
Stability of concatenated traveling waves: alternate approaches. Zbl 1353.35101
Lin, Xiao-Biao; Schecter, Stephen
1
2015
Transonic evaporation waves in a spherically symmetric nozzle. Zbl 1307.35231
Lin, Xiaobiao; Wechselberger, Martin
5
2014
Traveling wave solutions in coupled Chua’s circuits. I: Periodic solutions. Zbl 1307.34025
Chow, Shui-Nee; Jiang, Ming; Lin, Xiaobiao
4
2013
Stability of standing waves for monostable reaction-convection equations in a large bounded domain with boundary conditions. Zbl 1323.35090
Lin, Xiao-Biao
2
2013
Standing waves for phase transitions in a spherically symmetric nozzle. Zbl 1242.76330
Fan, Haitao; Lin, Xiao-Biao
3
2012
A dynamical systems approach to traveling wave solutions for liquid/vapor phase transition. Zbl 1263.35061
Fan, Haitao; Lin, Xiao-Biao
2
2012
Traveling wave solutions for a predator-prey system with sigmoidal response function. Zbl 1252.34048
Lin, Xiaobiao; Weng, Peixuan; Wu, Chufen
42
2011
Collapsing and explosion waves in phase transitions with metastability, existence, stability and related Riemann problems. Zbl 1203.35061
Fan, Haitao; Lin, Xiao-Biao
1
2010
Algebraic dichotomies with an application to the stability of Riemann solutions of conservation laws. Zbl 1192.34064
Lin, Xiao-Biao
5
2009
Gearhart-Prüss theorem and linear stability for Riemann solutions of conservation laws. Zbl 1132.35010
Lin, Xiao-Biao
1
2007
Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain. Zbl 1096.65106
Lai, Ming-Chih; Li, Zhilin; Lin, Xiaobiao
6
2006
Slow eigenvalues of self-similar solutions of the Dafermos regularization of a system of conservation laws: an analytic approach. Zbl 1098.35102
Lin, Xiao-Biao
2
2006
\(L^2\) semigroup and linear stability for Riemann solutions of conservation laws. Zbl 1113.35124
Lin, Xiaobiao
3
2005
Analytic semigroup generated by the linearization of a Riemann-Dafermos solution. Zbl 1073.35160
Lin, Xiao-Biao
2
2004
Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws. Zbl 1056.35112
Lin, Xiao-Biao; Schecter, Stephen
10
2003
Multistage evolutionary model for carcinogenesis mutations. Zbl 1014.92018
Ahangar, Reza; Lin, Xiao-Biao
3
2003
Heteroclinic and periodic cycles in a perturbed convection model. Zbl 1013.34041
Lin, Xiao-Biao; Vivancos, Ignacio B.
1
2002
Construction and asymptotic stability of structurally stable internal layer solutions. Zbl 0986.34043
Lin, Xiao-Biao
13
2001
Generalized Rankine-Hugoniot condition and shock solutions for quasilinear hyperbolic systems. Zbl 0978.35032
Lin, Xiao-Biao
1
2000
Multiple internal layer solutions generated by spatially oscillatory perturbations. Zbl 0978.35019
Hale, Jack K.; Lin, Xiao-Biao
7
1999
Fatigue growth simulation for cracks in notched and unnotched round bars. Zbl 0899.73423
Lin, X. B.; Smith, R. A.
1
1998
Homoclinic bifurcations with weakly expanding center manifolds. Zbl 0873.34031
Lin, Xiao-Biao
6
1996
Shadowing matching errors for wave-front-like solutions. Zbl 0864.35010
Lin, Xiao-Biao
6
1996
Local and global existence of multiple waves near formal approximations. Zbl 0855.35009
Lin, Xiao-Biao
5
1996
Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system. Zbl 0852.35012
Lin, Xiao-Biao
4
1996
Improved bicharacteristic schemes for two-dimensional elastodynamic equations. Zbl 0833.73073
Lin, X.; Ballman, J.
7
1995
Exponential dichotomies in intermediate spaces with applications to a diffusively perturbed predator-prey model. Zbl 0806.35078
Lin, Xiaobiao
13
1994
Exponential dichotomy and stability of long periodic solutions in predator-prey models with diffusion. Zbl 0823.35098
Lin, X. B.
1
1992
Smooth invariant foliations in infinite dimensional spaces. Zbl 0749.58043
Chow, Shui-Nee; Lin, Xiao-Biao; Lu, Kening
69
1991
Using Melnikov’s method to solve Silnikov’s problems. Zbl 0714.34070
Lin, Xiao-Biao
77
1990
Bifurcation of a homoclinic orbit with a saddle-node equilibrium. Zbl 0727.58026
Chow, Shuinee; Lin, Xiaobiao
31
1990
Heteroclinic bifurcation and singularly perturbed boundary value problems. Zbl 0708.34017
Lin, Xiao-Biao
15
1990
Bifurcation analysis on a coral-starfish model. Zbl 0721.34038
Antonelli, P. L.; Lin, X.
1
1990
A shadowing lemma with applications to semilinear parabolic equations. Zbl 0696.34033
Chow, Shui-Nee; Lin, Xiao-Biao; Palmer, Kenneth J.
22
1989
Shadowing lemma and singularly perturbed boundary value problems. Zbl 0686.34059
Lin, Xiaobiao
20
1989
Transition layers for singularly perturbed delay differential equations with monotone nonlinearities. Zbl 0684.34071
Chow, Shui-Nee; Lin, Xiao-Biao; Mallet-Paret, John
16
1989
A shadowing lemma for maps in infinite dimensions. Zbl 0689.34041
Chow, Shui-Nee; Lin, Xiao-Biao; Palmer, Kenneth J.
1
1989
Upper semicontinuity of attractors for approximations of semigroups and partial differential equations. Zbl 0666.35013
Hale, Jack K.; Lin, Xiao-Biao; Raugel, Geneviève
66
1988
A multiplicity theorem for hyperbolic systems. Zbl 0679.34077
Neves, Aloisio Freiria; Lin, Xiaobiao
7
1988
Another brief proof of the Sylvester theorem. Zbl 0663.51008
Lin, X. B.
1
1988
Exponential dichotomies and homoclinic orbits in functional differential equations. Zbl 0589.34055
Lin, Xiaobiao
56
1986
Heteroclinic orbits for retarded functional differential equations. Zbl 0611.34074
Hale, Jack K.; Lin, X.-B.
53
1986
Symbolic dynamics and nonlinear semiflows. Zbl 0632.58027
Hale, Jack K.; Lin, Xiao-Biao
25
1986
Examples of transverse homoclinic orbits in delay equations. Zbl 0613.34060
Hale, Jack K.; Lin, Xiao-Biao
6
1986
all top 5

Cited by 617 Authors

22 Lin, Xiaobiao
19 Lu, Kening
14 Zhang, Weinian
12 Sandstede, Björn
11 Battelli, Flaviano
11 Hale, Jack Kenneth
10 Dragičević, Davor
9 Shen, Wenxian
8 Zhu, Changrong
7 Barreira, Luis Manuel
7 Huang, Wenzhang
7 Liu, Xingbo
7 Raugel, Geneviève
7 Shen, Jun
7 Valls Anglés, Cláudia
6 Bates, Peter W.
6 Duan, Jinqiao
6 Fečkan, Michal
6 Krauskopf, Bernd
6 Langa, Jose’ Antonio
6 Ni, Mingkang
6 Zeng, Chongchun
5 Backes, Lucas H.
5 Champneys, Alan R.
5 Geng, Fengjie
5 Hsu, Cheng-Hsiung
5 Liu, Weishi
5 Nolasco de Carvalho, Alexandre
5 Osinga, Hinke Maria
5 Schecter, Stephen
5 Scheel, Arnd
5 Van Vleck, Erik S.
5 Walther, Hans-Otto
5 Wang, Bixiang
5 Wang, Yi
5 Zhou, Linfeng
5 Zhou, Shengfan
5 Zhu, Deming
4 Brunovský, Pavol
4 Deng, Bo
4 Homburg, Ale Jan
4 Joly, Romain
4 Kloeden, Peter Eris
4 Knobloch, Jürgen
4 Lani-Wayda, Bernhard
4 Li, Ji
4 Lin, Guo
4 Magal, Pierre
4 Mallet-Paret, John Joseph
4 Palmer, Kenneth James
4 Parker, Ross
4 Poláčik, Peter
4 Pötzsche, Christian
4 Rademacher, Jens Diederich Michael
4 Robinson, James Cooper
4 Schmalfuß, Björn
4 Trofimchuk, Sergei I.
4 Wu, Chufen
4 Zhang, Tianran
4 Zhao, Caidi
4 Zhao, Junyilang
3 Aguirre, Pablo
3 Ai, Shangbing
3 Beyn, Wolf-Jürgen
3 Carter, Paul M.
3 Chow, Shui-Nee
3 de Rijk, Björn
3 Ding, Xiaoquan
3 Foryś, Urszula
3 Jia, Xiaoyao
3 Jones, Christopher K. R. T.
3 Kaper, Tasso J.
3 Kevrekidis, Panayotis G.
3 Lian, Zeng
3 Long, Bin
3 Luo, Guangping
3 Pan, Shuxia
3 Recke, Lutz
3 Ruan, Shigui
3 Schnaubelt, Roland
3 Seydi, Ousmane
3 Szmolyan, Peter
3 Weng, Peixuan
3 Wieczorek, Sebastian M.
3 Wu, Jianhong
3 Yanchuk, Sergiĭ Volodymyrovych
3 Yang, Meihua
3 Zhou, Dun
2 Aceves, Alejandro B.
2 Al-Nayef, Anwar A.
2 Arrieta, José M.
2 Ashwin, Peter
2 Boĭchuk, Oleksandr Andriĭovych
2 Bortolan, Matheus Cheque
2 Chueshov, Igor’ Dmitrievich
2 Da Mota, Jesus Carlos
2 Diamond, Phil
2 do Nascimento, Arnaldo Simal
2 Du, Yihong
2 Ezzinbi, Khalil
...and 517 more Authors
all top 5

Cited in 118 Serials

104 Journal of Differential Equations
52 Journal of Dynamics and Differential Equations
22 Journal of Mathematical Analysis and Applications
15 Discrete and Continuous Dynamical Systems. Series B
13 Physica D
13 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
13 SIAM Journal on Applied Dynamical Systems
9 ZAMP. Zeitschrift für angewandte Mathematik und Physik
9 Transactions of the American Mathematical Society
8 Nonlinearity
8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
8 Discrete and Continuous Dynamical Systems
7 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
5 Proceedings of the American Mathematical Society
5 Journal of Nonlinear Science
5 Abstract and Applied Analysis
5 Journal of Computational Dynamics
5 Nonlinear Analysis. Theory, Methods & Applications
4 Computers & Mathematics with Applications
4 Journal of Computational Physics
4 Mathematics of Computation
4 Applied Mathematics and Computation
4 Journal of Functional Analysis
4 Chinese Annals of Mathematics. Series B
4 Applied Numerical Mathematics
4 Science China. Mathematics
3 Chaos, Solitons and Fractals
3 Applied Mathematics and Optimization
3 Memoirs of the American Mathematical Society
3 Numerische Mathematik
3 SIAM Journal on Mathematical Analysis
3 Journal of Mathematical Sciences (New York)
3 Journal of Difference Equations and Applications
3 Qualitative Theory of Dynamical Systems
3 Nonlinear Analysis. Real World Applications
3 Stochastics and Dynamics
3 Mediterranean Journal of Mathematics
3 Advances in Difference Equations
3 Discrete and Continuous Dynamical Systems. Series S
2 Archive for Rational Mechanics and Analysis
2 Computer Methods in Applied Mechanics and Engineering
2 Journal of Mathematical Biology
2 Journal of Mathematical Physics
2 Advances in Mathematics
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Journal of Computational and Applied Mathematics
2 Mathematische Annalen
2 Mathematische Nachrichten
2 Results in Mathematics
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Applied Mathematics Letters
2 Mathematical and Computer Modelling
2 Dynamics and Stability of Systems
2 European Journal of Applied Mathematics
2 Nonlinear Dynamics
2 Discrete Dynamics in Nature and Society
2 Communications in Nonlinear Science and Numerical Simulation
2 Acta Mathematica Scientia. Series B. (English Edition)
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
2 Communications on Pure and Applied Analysis
2 Boundary Value Problems
2 International Journal of Biomathematics
2 Open Mathematics
2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Bulletin of the Australian Mathematical Society
1 Computer Physics Communications
1 Communications on Pure and Applied Mathematics
1 Indian Journal of Pure & Applied Mathematics
1 Mathematical Methods in the Applied Sciences
1 Mathematical Notes
1 Rocky Mountain Journal of Mathematics
1 Ukrainian Mathematical Journal
1 The Annals of Probability
1 Archiv der Mathematik
1 Calcolo
1 Canadian Journal of Mathematics
1 Collectanea Mathematica
1 Computing
1 Dissertationes Mathematicae
1 Fundamenta Mathematicae
1 Integral Equations and Operator Theory
1 Inventiones Mathematicae
1 Journal of Soviet Mathematics
1 Mathematics and Computers in Simulation
1 Monatshefte für Mathematik
1 SIAM Journal on Control and Optimization
1 Ergodic Theory and Dynamical Systems
1 Applied Mathematics and Mechanics. (English Edition)
1 Acta Mathematica Hungarica
1 Bulletin of the Iranian Mathematical Society
1 RAIRO. Modélisation Mathématique et Analyse Numérique
1 Journal of Economic Dynamics & Control
1 Aequationes Mathematicae
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 SIAM Journal on Applied Mathematics
1 Acta Mathematica Sinica. New Series
1 Indagationes Mathematicae. New Series
1 Computational and Applied Mathematics
1 Bulletin des Sciences Mathématiques
1 Advances in Computational Mathematics
...and 18 more Serials
all top 5

Cited in 37 Fields

226 Ordinary differential equations (34-XX)
224 Partial differential equations (35-XX)
207 Dynamical systems and ergodic theory (37-XX)
65 Biology and other natural sciences (92-XX)
40 Numerical analysis (65-XX)
32 Operator theory (47-XX)
26 Fluid mechanics (76-XX)
22 Probability theory and stochastic processes (60-XX)
13 Difference and functional equations (39-XX)
13 Global analysis, analysis on manifolds (58-XX)
9 Optics, electromagnetic theory (78-XX)
7 Mechanics of deformable solids (74-XX)
7 Systems theory; control (93-XX)
5 Mechanics of particles and systems (70-XX)
4 Integral equations (45-XX)
4 Classical thermodynamics, heat transfer (80-XX)
4 Statistical mechanics, structure of matter (82-XX)
3 History and biography (01-XX)
3 Functional analysis (46-XX)
3 Calculus of variations and optimal control; optimization (49-XX)
3 Computer science (68-XX)
2 General and overarching topics; collections (00-XX)
2 Manifolds and cell complexes (57-XX)
2 Geophysics (86-XX)
2 Operations research, mathematical programming (90-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Measure and integration (28-XX)
1 Functions of a complex variable (30-XX)
1 Approximations and expansions (41-XX)
1 Integral transforms, operational calculus (44-XX)
1 Differential geometry (53-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Statistics (62-XX)
1 Quantum theory (81-XX)
1 Astronomy and astrophysics (85-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year