Diffusion-Driven Instability in Reaction Diffusion Systems
نویسندگان
چکیده
For a stable matrix A with real entries, sufficient and necessary conditions for A D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction diffusion systems are discussed and an example is given to show applications. 2001 Academic Press
منابع مشابه
Characterization of Turing Diffusion-driven Instability on Evolving Domains
In this paper we establish a general theoretical framework for Turing diffusion-driven instability for reaction-diffusion systems on time-dependent evolving domains. The main result is that Turing diffusion-driven instability for reaction-diffusion systems on evolving domains is characterised by Lyapunov exponents of the evolution family associated with the linearised system (obtained by linear...
متن کاملInstability 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 کاملAlmost sure exponential stability of stochastic reaction diffusion systems with Markovian jump
The stochastic reaction diffusion systems may suffer sudden shocks, in order to explain this phenomena, we use Markovian jumps to model stochastic reaction diffusion systems. In this paper, we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps. Under some reasonable conditions, we show that the trivial solution of stocha...
متن کاملA Methodology for Parameter Identification in Turing Systems
We introduce a general methodology for parameter identification in reaction-diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm is illustrated with the Schnakenberg and Gierer-Meinhardt reaction-diffusion systems using PDE constrained optimization techniques. A quadratic cost functional that measures t...
متن کاملInvestigating the Turing conditions for diffusion-driven instability in the presence of a binding immobile substrate.
Turing's diffusion-driven instability for the standard two species reaction-diffusion system is only achievable under well-known and rather restrictive conditions on both the diffusion rates and the kinetic parameters, which necessitates the pairing of a self-activator with a self-inhibitor. In this study we generalize the standard two-species model by considering the case where the reactants c...
متن کامل