Stable bound states of pulses in an excitable medium

DOI10.1016/S0167-2789(99)00136-0zbMath0945.34032OpenAlexW2040458346MaRDI QIDQ1961679

Markus Bär, Ioannis G. Kevrekidis, Michal Or-Guil

Publication date: 19 September 2000

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(99)00136-0

zbMATH Keywords

stability analysispulsesnumerical simulationsexcitable mediumpulse interactionsmultiscale perturbation theorystable bound stateskinematic theory

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Reaction-diffusion equations (35K57) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Reaction effects in flows (76V05) Qualitative investigation and simulation of ordinary differential equation models (34C60) Multiple scale methods for ordinary differential equations (34E13)

Related Items (14)

Continuation of spiral waves ⋮ Unusual spiral wave dynamics in the Kessler-Levine model of an excitable medium ⋮ Convergent analytic solutions for homoclinic orbits in reversible and non-reversible systems ⋮ Coherent structures near the boundary between excitable and oscillatory media ⋮ Heteroclinic contours and self-replicated solitary waves in a reaction-diffusion lattice with complex threshold excitation ⋮ Modulated amplitude waves in the cubic-quintic Ginzburg-Landau equation ⋮ Anomalous dispersion in the Belousov-Zhabotinsky reaction: experiments and modeling ⋮ A computer-assisted study of pulse dynamics in anisotropic media ⋮ Composite ``zigzag structures in the 1D complex Ginzburg-Landau equation ⋮ Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation ⋮ Traveling waves in the Baer and Rinzel model of spine studded dendritic tissue ⋮ Alternans and the influence of ionic channel modifications: Cardiac three–dimensional simulations and one-dimensional numerical bifurcation analysis ⋮ Double-wave reentry in excitable media ⋮ Nonlinear analysis of the Eckhaus instability: Modulated amplitude waves and phase chaos with nonzero average phase gradient

Uses Software

• AUTO
• AUTO-86

Cites Work

• Non-equilibrium dynamics in chemical systems. Proceedings of the International Symposium, Bordeaux, France, September 3-7, 1984
• Singular perturbation theory of traveling waves in excitable media (A review)
• Pulse bifurcation and transition to spatiotemporal chaos in an excitable reaction-diffusion model
• Existence and stability of \(N\)-pulses on optical fibers with phase-sensitive amplifiers
• Numerical bifurcation and stability analysis of solitary pulses in an excitable reaction-diffusion medium
• Pulse Dynamics in an Unstable Medium
• Patterns of Propagating Pulses
• Generation and Suppression of Radiation by Solitary Pulses
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
• Multisoliton Solutions of the Complex Ginzburg-Landau Equation

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