Related papers: Oscillatory instability in super-diffusive reactio…
We consider a model proposed by one of the authors for a type of plastic instability found in creep experiments which reproduces a number of experimentally observed features. The model consists of three coupled non-linear differential…
We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The…
A diffusive ratio-dependent Holling-Tanner system subject to Neumann boundary conditions is considered. The existence of multiple bifurcations, including Turing-Hopf bifurcation, Turing-Truing bifurcation, Hopf-double-Turing bifurcation and…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those diffusions, the…
We study pattern formation in a complex Swift Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions can be written as a euclideen Schr\"odinger equation in which the wave function is the probability distribution and the Hamiltonian is…
A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities is considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
For two-dimensional autonomous linear incommensurate fractional-order dynamical systems with Caputo derivatives of different orders, necessary and sufficient conditions are obtained for the asymptotic stability and instability of the null…
The propagating chemical fronts found in cubic autocatalytic reaction-diffusion processes are studied. Simulations of the reaction-diffusion equation near to and far from the onset of the front instability are performed and the structure…
This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…
The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity,…
For delayed reaction-diffusion Schnakenberg systems with Neumann boundary conditions, critical conditions for Turing instability are derived, which are necessary and sufficient. And existence conditions for Turing, Hopf and Turing-Hopf…