Breathing pulses in singularly perturbed reaction-diffusion systems
From MaRDI portal
Publication:2944161
DOI10.1088/0951-7715/28/7/2211zbMath1335.37054OpenAlexW2279446551MaRDI QIDQ2944161
Publication date: 28 August 2015
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/6eeeee4c8cfd012dcea812038d106e07ffcb34d6
singular perturbationHopf bifurcationreaction-diffusionoscillonbreathing pulsecentre manifold expansion
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Pattern formations in context of PDEs (35B36)
Related Items
Oscillatory translational instabilities of spot patterns in the Schnakenberg system on general 2D domains ⋮ Hopf bifurcation from spike solutions for the weak coupling Gierer–Meinhardt system ⋮ Spectra and Stability of Spatially Periodic Pulse Patterns: Evans Function Factorization via Riccati Transformation ⋮ Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities ⋮ Anomalous Scaling of Hopf Bifurcation Thresholds for the Stability of Localized Spot Patterns for Reaction-Diffusion Systems in Two Dimensions ⋮ Dynamics of Meandering Spiral Waves with Weak Lattice Perturbations ⋮ Robust stability of multicomponent membranes: the role of glycolipids ⋮ The dynamics of disappearing pulses in a singularly perturbed reaction-diffusion system with parameters that vary in time and space ⋮ Spectra and Stability of Spatially Periodic Pulse Patterns II: The Critical Spectral Curve ⋮ Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical ⋮ Destabilization Mechanisms of Periodic Pulse Patterns Near a Homoclinic Limit ⋮ Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system ⋮ Stable and unstable periodic spiky solutions for the Gray-Scott system and the Schnakenberg system ⋮ Weakly Nonlinear Analysis of Peanut-Shaped Deformations for Localized Spots of Singularly Perturbed Reaction-Diffusion Systems ⋮ Localised spatial structures in the Thomas model ⋮ Complex oscillatory motion of multiple spikes in a three-component Schnakenberg system