The bifurcation analysis of Turing pattern formation induced by delay and diffusion in the Schnakenberg system
DOI10.3934/dcdsb.2017031zbMath1360.35016OpenAlexW2563603036MaRDI QIDQ524023
Eamonn A. Gaffney, Sungrim Seirin Lee, Feng-Qi Yi
Publication date: 25 April 2017
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdsb.2017031
Hopf bifurcationSchnakenberg modelnormal form methoddiffusion driven instabilitydelay and diffusiondelay-diffusion driven instability
Developmental biology, pattern formation (92C15) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Pattern formations in context of PDEs (35B36)
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Cites Work
- Gene expression time delays and Turing pattern formation systems
- The dynamics of Turing patterns for morphogen-regulated growing domains with cellular response delays
- The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems
- Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays
- A note on Hopf bifurcations in a delayed diffusive Lotka-Volterra predator-prey system
- Discrete delay, distributed delay and stability switches
- Instability of homogeneous periodic solutions of parabolic-delay equations
- Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
- Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
- Time delay-induced instabilities and Hopf bifurcations in general reaction-diffusion systems
- The effect of delay on a diffusive predator-prey system with Holling type-II predator functional response
- Mixed-mode pattern in \textit{Doublefoot} mutant mouse limb -- Turing reaction-diffusion model on a growing domain during limb development
- Global attractivity of equilibrium in Gierer-Meinhardt system with activator production saturation and gene expression time delays
- Interaction of diffusion and delay
- Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters
- The Effects of Harvesting and Time Delay on Predator-prey Systems with Holling Type II Functional Response
- Destabilization of periodic solutions arising in delay-diffusion systems in several space dimensions
- Turing instability and travelling waves in diffusive plankton models with delayed nutrient recycling
- Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays
- The chemical basis of morphogenesis
- Normal forms and Hopf bifurcation for partial differential equations with delays
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