Linear Stability of Fractional Reaction - Diffusion Systems
نویسندگان
چکیده
منابع مشابه
Nonlinear oscillations and stability domains in fractional reaction-diffusion systems
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives. It ...
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 کاملAnomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.
We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative o...
متن کاملCross-diffusion Induced Instability and Stability in Reaction-diffusion Systems
In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize a uniform equilibrium which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize a uniform equilibrium which...
متن کاملA Nonlocal Eigenvalue Problem and the Stability of Spikes for Reaction-diffusion Systems with fractional Reaction Rates
We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel’kov model, the Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding...
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 Modelling of Natural Phenomena
سال: 2007
ISSN: 0973-5348
DOI: 10.1051/mmnp:2008020