Robust Pulse Generators in an Excitable Medium with Jump-Type Heterogeneity

DOI10.1137/13091261XzbMath1331.35040MaRDI QIDQ2940716

Masaaki Yadome, Takashi Teramoto, Yasumasa Nishiura

Publication date: 20 January 2015

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

dissipative solutionsglobal bifurcation structurehomoclinic gluing bifurcation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Second-order parabolic systems (35K40) Traveling wave solutions (35C07) Pattern formations in context of PDEs (35B36)

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Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional ⋮ Wave Reflections in Excitable Media Linked to Existence and Stability of One-Dimensional Spiral Waves ⋮ Arbitrarily weak head-on collision can induce annihilation: the role of hidden instabilities ⋮ Reduction approach to the dynamics of interacting front solutions in a bistable reaction-diffusion system and its application to heterogeneous media ⋮ Pinned solutions in a heterogeneous three-component FitzHugh-Nagumo model ⋮ Traveling pulses with oscillatory tails, figure-eight-like stack of isolas, and dynamics in heterogeneous media

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