Numerical bifurcation and stability analysis of solitary pulses in an excitable reaction-diffusion medium

DOI10.1016/S0045-7825(98)00198-4zbMath0941.65131MaRDI QIDQ1965145

Yanyan Li

Publication date: 20 July 2000

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

chaotic dynamicsHopf bifurcationsfeedback controlreaction-diffusion modeltravelling waveinstabilitiesharmonic balancechemical reactor systemplanar cubic system

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Chemically reacting flows (80A32) Numerical chaos (65P20) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30) Numerical nonlinear stabilities in dynamical systems (65P40) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50)

Related Items (12)

CONTROLLING CHAOS TO A CLASS OF PDEs BY APPLYING INVARIANT MANIFOLD AND STRUCTURE STABILITY THEORY ⋮ Using Lin's method to solve Bykov's problems ⋮ Analysis of the T-point-Hopf bifurcation in the Lorenz system ⋮ Propagation failures, breathing pulses, and backfiring in an excitable reaction-diffusion system ⋮ Stable bound states of pulses in an excitable medium ⋮ Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible? ⋮ A computer-assisted study of pulse dynamics in anisotropic media ⋮ Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies ⋮ Accumulations of \(T\)-points in a model for solitary pulses in an excitable reaction-diffusion medium ⋮ Alternans and the influence of ionic channel modifications: Cardiac three–dimensional simulations and one-dimensional numerical bifurcation analysis ⋮ Pulse Replication and Accumulation of Eigenvalues ⋮ Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit

Uses Software

• AUTO

Cites Work

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