Unstable wavetrains and chaotic wakes in reaction-diffusion systems of \(\lambda-\omega\) type

DOI10.1016/0167-2789(94)00224-EzbMath0900.35194OpenAlexW1970648277MaRDI QIDQ1346882

Jonathan A. Sherratt

Publication date: 27 March 1995

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(94)00224-e

zbMATH Keywords

complex sequence of bifurcationsirregular wakesone-dimensional finite spatial domain

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32)

Related Items (11)

A comparison of two numerical methods for oscillatory reaction-diffusion systems ⋮ Periodic travelling waves in a family of deterministic cellular automata ⋮ Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations ⋮ Transition fronts and localized structures in bistable reaction-diffusion equations ⋮ Oscillation and pattern formation in a system of self-regulating cells ⋮ Invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave ⋮ Influence of self- and cross-diffusion on wave train solutions of reaction-diffusion systems ⋮ Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion ⋮ Dynamics of diffusive modified Previte-Hoffman food web model ⋮ Existence of epidemic waves in a disease transmission model with two-habitat population ⋮ Oscillatory and chaotic wakes behind moving boundaries in reaction–diffusion systems

Cites Work

• Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems
• Stability of spatially homogeneous periodic solutions of reaction- diffusion equations
• Irregular wakes in reaction-diffusion waves
• Two boundary value problems for the Ginzburg-Landau equation
• Rotating Spiral Waves in Reaction-Diffusion Systems: Phase Singularities of Multi-Armed Waves
• Dynamics of Perturbed Wavetrain Solutions to the Ginzburg-Landau Equation
• Stability of Limit Cycle Solutions of Reaction-Diffusion Equations
• Plane Wave Solutions to Reaction-Diffusion Equations
• The amplitude of periodic plane waves depends on initial conditions in a variety of lambda - omega systems
• On the speed of amplitude transition waves in reaction-diffusion systems of λ−ω type
• Spiral Waves in Reaction-Diffusion Equations
• The automatic integration of ordinary differential equations

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