Spike patterns in a reaction-diffusion ODE model with Turing instability
نویسندگان
چکیده
منابع مشابه
Instability of turing patterns in reaction-diffusion-ODE systems
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis o...
متن کاملOscillatory Turing Patterns in a Simple Reaction-Diffusion System
Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way as to produce steady-state inhomogeneous spatial patterns of chemical concentrations. We consider a simple two-variable reaction-diffusion system and find there is a spatio-temporally oscillating solution (STOS) in parameter regions where linear analysis predicts a pure Turing instability and no Hopf ...
متن کاملSpatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes.
Spatial resonances leading to superlattice hexagonal patterns, known as "black-eyes," and superposition patterns combining stripes and/or spots are studied in a reaction-diffusion model of two interacting Turing modes with different wavelengths. A three-phase oscillatory interlacing hexagonal lattice pattern is also found, and its appearance is attributed to resonance between a Turing mode and ...
متن کاملHopf bifurcation and Turing instability in the reaction–diffusion Holling–Tanner predator–prey model
The reaction–diffusion Holling–Tanner predator–prey model with Neumann boundary condition is considered. We perform a detailed stability and Hopf bifurcation analysis and derive conditions for determining the direction of bifurcation and the stability of the bifurcating periodic solution. For partial differential equation (PDE), we consider the Turing instability of the equilibrium solutions an...
متن کاملStable squares and other oscillatory turing patterns in a reaction-diffusion model.
We study the Brusselator reaction-diffusion model under conditions where the Hopf mode is supercritical and the Turing band is subcritical. Oscillating Turing patterns arise in the system when bulk oscillations lose their stability to spatial perturbations. Spatially uniform external periodic forcing can generate oscillating Turing patterns when both the Turing and Hopf modes are subcritical in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Methods in the Applied Sciences
سال: 2013
ISSN: 0170-4214
DOI: 10.1002/mma.2899