A Turing-Hopf bifurcation scenario for pattern formation on growing domains

DOI10.1007/s11538-016-0189-6zbMath1361.92009OpenAlexW2466494977WikidataQ50610513 ScholiaQ50610513MaRDI QIDQ517986

Jorge A. Castillo, Faustino Sánchez-Garduño, Pablo Padilla

Publication date: 28 March 2017

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11538-016-0189-6

zbMATH Keywords

targetFitzHugh-Nagumo modelgrowing domainTuring-Hopf bifurcationspiral and turbulent-like patterns

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Developmental biology, pattern formation (92C15)

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Cites Work

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• Turing instabilities and patterns near a Hopf bifurcation
• Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains
• Pattern formation, long-term transients, and the Turing-Hopf bifurcation in a space- and time-discrete predator-prey system
• Hopf bifurcation and Turing instability in spatial homogeneous and inhomogeneous predator-prey models
• Attractivity and bifurcation for nonautonomous dynamical systems
• Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• The effect of growth and curvature on pattern formation
• Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations
• The chemical basis of morphogenesis