Waves in a simple, excitable or oscillatory, reaction-diffusion model

DOI10.1007/BF00276897zbMath0456.92025OpenAlexW1991769667WikidataQ113909048 ScholiaQ113909048MaRDI QIDQ1150547

John Rinzel, G. Bard Ermentrout

Publication date: 1981

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00276897

zbMATH Keywords

solitary wavesoscillationringsreaction-diffusion modelexcitabilitypropagating wave trainspulse waves

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Periodic solutions to ordinary differential equations (34C25) Stability in context of PDEs (35B35) General biology and biomathematics (92B05) Other special methods applied to PDEs (35A25) Chemistry (92Exx)

Related Items (8)

Rotating waves in simple scalar excitable media: approximations and numerical solutions ⋮ Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities ⋮ Traveling Pulses in a Nonlocal Equation Arising Near a Saddle-Node Infinite Cycle Bifurcation ⋮ n:m phase-locking of weakly coupled oscillators ⋮ Coherent structures near the boundary between excitable and oscillatory media ⋮ Bifurcation structure of rotating wave solutions of the Fitzhugh-Nagumo equations ⋮ Waves and Patterns on Regular Graphs ⋮ The behavior of rings of coupled oscillators

Cites Work

• Unnamed Item
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Pattern formation and periodic structures in systems modeled by reaction-diffusion equations
• Plane Wave Solutions to Reaction-Diffusion Equations

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