Stripe and spot patterns for the Gierer-Meinhardt model with saturated activator production

DOI10.1016/j.jmaa.2017.01.019zbMath1357.35035OpenAlexW2574151704MaRDI QIDQ509031

You Li, Xiaojie Hou, Jin-Liang Wang

Publication date: 8 February 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.01.019

zbMATH Keywords

Hopf bifurcationTuring patternssupercriticalsubcriticalunique positive equilibrium

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Pattern formations in context of PDEs (35B36)

Related Items (15)

Dynamics of a depletion-type Gierer-Meinhardt model with Langmuir-Hinshelwood reaction scheme ⋮ Bifurcation and Turing patterns of reaction-diffusion activator-inhibitor model ⋮ Turing–Hopf Bifurcation in Diffusive Gierer–Meinhardt Model ⋮ Spatiotemporal patterns induced by four mechanisms in a tussock sedge model with discrete time and space variables ⋮ Unnamed Item ⋮ Hopf Bifurcation Analysis in a Gierer–Meinhardt Activator–Inhibitor Model ⋮ Hopf Bifurcation and Self-Organization Pattern of a Modified Brusselator Model ⋮ Analysis of the Hopf bifurcation in a diffusive Gierer-Meinhardt model ⋮ Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system ⋮ Supercritical Hopf bifurcation and Turing patterns for an activator and inhibitor model with different sources ⋮ Bifurcation, Chaos and Turing Instability Analysis for a Space-Time Discrete Toxic Phytoplankton-Zooplankton Model with Self-Diffusion ⋮ Stability and Hopf Bifurcation Analysis of a Reduced Gierer–Meinhardt Model ⋮ Pattern Dynamics in a Diffusive Gierer–Meinhardt Model ⋮ Spatiotemporal Dynamics and Pattern Formations of an Activator-Substrate Model with Double Saturation Terms ⋮ Patterns in a freshwater tussock sedge model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Diffusion-driven instability and bifurcation in the Lengyel-Epstein system
• Geometric theory of semilinear parabolic equations
• Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems
• 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
• The Hopf bifurcation theorem in infinite dimensions
• Stability of spatially homogeneous periodic solutions of reaction- diffusion equations
• Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model
• Pulses in a Gierer--Meinhardt Equation with a Slow Nonlinearity
• MULTIPLE BIFURCATION ANALYSIS AND SPATIOTEMPORAL PATTERNS IN A 1-D GIERER–MEINHARDT MODEL OF MORPHOGENESIS
• The chemical basis of morphogenesis
• Hopf bifurcation of spike solutions for the shadow GiererMeinhardt model
• Hopf bifurcation and Turing instability in the reaction-diffusion Holling-Tanner predator-prey model
• Stripe and Spot Patterns for General Gierer–Meinhardt Model with Common Sources

This page was built for publication: Stripe and spot patterns for the Gierer-Meinhardt model with saturated activator production