Traveling wave solutions for planar lattice differential systems with applications to neural networks

DOI10.1006/jdeq.2001.4109zbMath1221.37162OpenAlexW2078321203MaRDI QIDQ1614746

Shiwang Ma, Jianhong Wu, Xiao-Xin Liao

Publication date: 8 September 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4109

zbMATH Keywords

neural networkfixed-point theoremperiodic traveling wavetraveling wave frontequivariant bifurcation theory\(S^1\)-degreeplanar lattice differential system

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Dynamical systems in biology (37N25) Functional-differential equations in abstract spaces (34K30) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)

Related Items (10)

Asymptotic speed of propagation and traveling wavefronts in a non-local delayed lattice differential equation ⋮ DIVERSITY OF TRAVELING WAVE SOLUTIONS IN DELAYED CELLULAR NEURAL NETWORKS ⋮ Wave propagation in a two-dimensional lattice dynamical system with global interaction ⋮ Travelling wavefronts in nonlocal diffusion equations with nonlocal delay effects ⋮ Propagation and its failure in a lattice delayed differential equation with global interaction ⋮ EXISTENCE OF MONOTONIC TRAVELING WAVES IN LATTICE DYNAMICAL SYSTEMS ⋮ Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities ⋮ Rigorous verification of Hopf bifurcations in functional differential equations of mixed type ⋮ Existence of traveling wave solutions in a stage structured cooperative system on higher-dimensional lattices ⋮ Existence, uniqueness and stability of travelling waves in a discrete reaction --- diffusion monostable equation with delay

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