Spatiotemporal stability of periodic travelling waves in a heteroclinic-cycle model

DOI10.1088/1361-6544/ac0126zbMath1475.37085arXiv1911.10447OpenAlexW3180579903MaRDI QIDQ5000664

Hinke M. Osinga, Cris R. Hasan, Claire M. Postlethwaite, Alastair M. Rucklidge

Publication date: 15 July 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.10447

zbMATH Keywords

spiral wavesheteroclinic cyclesEckhaus instabilitystability of traveling wavesBusse balloonrock-paper-scissors model

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Computational methods for bifurcation problems in dynamical systems (37M20) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Traveling wave solutions (35C07) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (2)

Order and Disorder in a Cyclically Competitive Ecological Community ⋮ Travelling waves and heteroclinic networks in models of spatially-extended cyclic competition

Uses Software

• AUTO
• AUTO-07P

Cites Work

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• Evolutionary game theory: theoretical concepts and applications to microbial communities
• Exponential time differencing for stiff systems
• Continuation of spiral waves
• The accumulation of eigenvalues in a stability problem
• Stability of periodic traveling waves in the Aliev-Panfilov reaction-diffusion system
• Computing absolute and essential spectra using continuation
• Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations
• Continuation-based Computation of Global Isochrons
• A Lin's method approach to finding and continuing heteroclinic connections involving periodic orbits
• Nonlinear Aspects of Competition Between Three Species
• Gluing unstable fronts and backs together can produce stable pulses
• Striped pattern selection by advective reaction-diffusion systems: Resilience of banded vegetation on slopes
• A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock–Paper–Scissors
• Numerical continuation of spiral waves in heteroclinic networks of cyclic dominance
• On the Stability of Two‐Dimensional Convection in a Layer Heated from Below

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