Related papers: Oscillatory instability in super-diffusive reactio…
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and…
We consider networks of reaction-diffusion systems of Hodgkin-Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as existence of invariant regions and of the attractor. Then,…
We consider a class of nonlinear fractional equations having the Caputo fractional derivative of the time variable $t$, the fractional order of the self-adjoint positive definite unbounded operator in a Hilbert space and a singular…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
Three dimensional roll-type double-diffusive convection in a horizontally infinite layer of an uncompressible liquid is considered in the neighborhood of Hopf bifurcation points. A system of amplitude equations for the variations of…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction-diffusion systems, viz., the Fisher equation and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of our…
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from…
We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented.…
The diffusion system with time-fractional order derivative is of great importance mathematically due to the nonlocal property of the fractional order derivative, which can be applied to model the physical phenomena with memory effects. We…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
The reaction-diffusion system of Fitzhugh Nagumo is considered. The initial- boundary problems with Neumann and Dirichlet conditions are analyzed. By means of an equivalent semilinear integrodifferential equation which characterizes several…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…