Consistency of local dynamics and bifurcation of continuous-time dynamical systems and their numerical discretizations

DOI10.1080/10236199808808127zbMath0909.65043OpenAlexW2042729829MaRDI QIDQ4209755

Xin Wang, Qingnan Li, Edward K. Blum

Publication date: 22 March 1999

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236199808808127

zbMATH Keywords

consistencydynamical systemsHopf bifurcationRunge-Kutta methodsEuler methodone-step methodhyperbolic fixed pointstopological conjugate

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Dynamical systems and ergodic theory (37-XX)

Related Items (6)

Discretizing the fold bifurcation - a conjugacy result ⋮ Asymptotic behaviors of solutions to quasilinear elliptic equation with Hardy potential and critical Sobolev exponent ⋮ Preservation of Takens-Bogdanov bifurcations for delay differential equations by Euler discretization ⋮ Various closeness results in discretized bifurcations ⋮ Discretizing dynamical systems with generalized Hopf bifurcations ⋮ DISCRETIZING BIFURCATION DIAGRAMS NEAR CODIMENSION TWO SINGULARITIES

Uses Software

• AUTO-86

Cites Work

• Singularities and groups in bifurcation theory. Volume I
• Invariant curves of one-step methods
• Discrete-time versus continuous-time models of neural networks
• Singularities and groups in bifurcation theory. Volume II
• On invariant closed curves for one-step methods
• Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points
• On a dangerous property of methods for stiff differential equations
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS
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