Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems
From MaRDI portal
Publication:4205791
DOI10.1016/0362-546X(89)90061-8zbMath0687.35008OpenAlexW2031256957MaRDI QIDQ4205791
Hideo Ikeda, Yasumasa Nishiura, Masayasu Mimura
Publication date: 1989
Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0362-546x(89)90061-8
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32)
Related Items
Traveling waves for the Fitzhugh-Nagumo system on an infinite channel, Heteroclinic and homoclinic bifurcations in bistable reaction diffusion systems, Existence and stability of pulse wave bifurcated from front and back waves in bistable reaction-diffusion systems, Singular perturbation and bifurcation of diffuse transition layers in inhomogeneous media. II, Existence of traveling wave solutions to reaction-diffusion-ODE systems with hysteresis, Arbitrarily weak head-on collision can induce annihilation: the role of hidden instabilities, Layers in the presence of conservation laws, Monostable-type travelling wave solutions of the diffusive FitzHugh-Nagumo-type system in \(\mathbb{R}^N\), Front dynamics in heterogeneous diffusive media, Front-bifurcations in reaction-diffusion systems with inhomogeneous parameter distributions, Order parameter equations for front transitions: Nonuniformly curved fronts, Singular limit approach to stability and bifurcation for bistable reaction diffusion systems, Lie group analysis and dynamical behavior for classical Boussinesq-Burgers system, Dynamics of front solutions in a specific reaction-diffusion system in one dimension, Multistability in Ecosystems: Concerns and Opportunities for Ecosystem Function in Variable Environments, Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I: The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics, Matched asymptotic expansion approach to pulse dynamics for a three-component reaction-diffusion system, Traveling fronts in an array of coupled symmetric bistable units, Existence of standing pulse solutions for an excitable activator- inhibitory system, Travelling wave solutions for reaction-diffusion equations, Traveling fronts bifurcating from stable layers in the presence of conservation laws, Parity-breaking front bifurcation in bistable media: link between discrete and continuous versions, Corrections to: ``Singular limit approach to stability and bifurcation for bistable reaction diffusion systems, The existence and stability of travelling waves with transition layers for some singular cross-diffusion systems, Pattern formation in consumer-finite resource reaction-diffusion systems, Boundary effects on localized structures in spatially extended systems, Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system, Travelling wave solutions to a generalized system of nerve equations, Localized patterns in reaction-diffusion systems, Multiple internal layer solutions generated by spatially oscillatory perturbations, Internal layer oscillations in FitzHugh-Nagumo equation
Cites Work
- Singular perturbation approach to traveling waves in competing and diffusing species models
- A remark on singular perturbation methods
- Boundary and interior transition layer phenomena for pairs of second- order differential equations
- The approach of solutions of nonlinear diffusion equations to travelling front solutions
- Asymptotic analysis of reaction-diffusion wave fronts
- Layer Oscillations in Reaction-Diffusion Systems
- Oscillatory Coexistence in the Chemostat: A Codimension Two Unfolding
- Propagation Phenomena in a Bistable Reaction-Diffusion System
- Stability of Singularly Perturbed Solutions to Systems of Reaction-Diffusion Equations