Layer Oscillations in Reaction-Diffusion Systems
From MaRDI portal
Publication:3032644
DOI10.1137/0149029zbMath0691.35009OpenAlexW2016962304MaRDI QIDQ3032644
Masayasu Mimura, Yasumasa Nishiura
Publication date: 1989
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0149029
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32)
Related Items (47)
Asymptotic behavior of solutions of an allen-cahn equation with a nonlocal term ⋮ Spherically symmetric internal layers for activator-inhibitor systems. I: Existence by a Lyapunov-Schmidt reduction ⋮ A Hopf bifurcation in a parabolic free boundary problem ⋮ A free boundary problem arising in some reacting–diffusing system ⋮ Spike-type contrast structures in reaction-diffusion systems ⋮ Classification of patterns in excitable systems with lateral inhibition ⋮ Heteroclinic and homoclinic bifurcations in bistable reaction diffusion systems ⋮ Pattern formation in coupled reaction-diffusion systems ⋮ Oscillations of fronts and front pairs in two- and three-component reaction-diffusion systems ⋮ Hopf bifurcation with the spatial average of an activator in a radially symmetric free boundary problem ⋮ Arbitrarily weak head-on collision can induce annihilation: the role of hidden instabilities ⋮ Higher-order resonances and instability of high-frequency WKB solutions ⋮ Oscillations of many interfaces in the near-shadow regime of two-component reaction-diffusion systems ⋮ Stability of front solutions in inhomogeneous media ⋮ An asymptotic study of the inductive pattern formation mechanism in Drosophila egg development ⋮ Necessity of internal and boundary bulk balance law for existence of interfaces for an elliptic system with nonlinear boundary condition ⋮ Stationary and oscillatory fronts in a two-component genetic regulatory network model ⋮ Effects on global coupling of an interface problem in an activator-inhibitor system. ⋮ Stability and characteristic wavelength of planar interfaces in the large diffusion limit of the inhibitor ⋮ Reduction approach to the dynamics of interacting front solutions in a bistable reaction-diffusion system and its application to heterogeneous media ⋮ Phase field models and sharp interface limits: Some differences in subtle situations ⋮ Singular limit approach to stability and bifurcation for bistable reaction diffusion systems ⋮ A stability index for steady state solutions of boundary value problems for parabolic systems ⋮ Matched asymptotic expansion approach to pulse dynamics for a three-component reaction-diffusion system ⋮ Galloping instability of viscous shock waves ⋮ Pattern selection in a general model of convection, diffusion and catalytic reaction ⋮ A Hopf bifurcation in a free boundary problem with inhomogeneous media ⋮ Dynamical system for animal coat pattern model ⋮ Corrections to: ``Phase field models and sharp interface limits: Some differences in subtle situations ⋮ Corrections to: ``Singular limit approach to stability and bifurcation for bistable reaction diffusion systems ⋮ A HOPF BIFURCATION IN A FREE BOUNDARY PROBLEM DEPENDING ON THE SPATIAL AVERAGE OF AN ACTIVATOR ⋮ Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system ⋮ Slow motion manifolds far from the attractor in multistable reaction-diffusion equations ⋮ Inhomogeneity-induced bifurcation of stationary and oscillatory pulses ⋮ The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime ⋮ Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system ⋮ Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model ⋮ Filtering of Spatial Bias and Noise Inputs by Spatially Structured Neural Networks ⋮ Stability Criteria for Reaction-Diffusion Systems with Skew-Gradient Structure ⋮ An interfacial approach to regional segregation of two competing species mediated by a predator ⋮ Singular Hopf-bifurcation in a chemical reaction-diffusion system ⋮ Localized patterns in reaction-diffusion systems ⋮ Standing Waves Joining with Turing Patterns in FitzHugh–Nagumo Type Systems ⋮ Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems ⋮ Complex oscillatory motion of multiple spikes in a three-component Schnakenberg system ⋮ Internal layer oscillations in FitzHugh-Nagumo equation ⋮ On the bifurcation curve for an elliptic system of FitzHugh-Nagumo type
This page was built for publication: Layer Oscillations in Reaction-Diffusion Systems
