Travelling wave fronts in reaction–diffusion systems with spatio-temporal delays

Abstract

This paper deals with the existence of travelling wave fronts in reaction-diffusion systems with spatio-temporal delays. Our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system. New iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions. Following this, the existence of travelling wave fronts for reaction-diffusion systems with spatio-temporal delays is established. Finally, we apply the main results to a single-species diffusive model with spatio-temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels.

Stability Analysis of a Reaction–Diffusion Equation with Spatiotemporal Delay and Dirichlet Boundary Condition

“…And it remains open that whether Hopf bifurcation could occur for Dirichlet boundary condition. We also remark that there are many results on the traveling wave solutions of reaction-diffusion models with nonlocal delay, (see References [1,7,[14][15][16][17]20] and the references therein).…”

Existence of Waves for a Nonlocal Reaction-Diffusion Equation

“…In some cases the interaction of the individuals in the population can be nonlocal. Some biological examples are considered in [11], [17], [18]. This can be for example plants that can distribute their pollen in some area around their location or biological cells which can send signalling molecules.…”

Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources

“…It is determined only by the diffusion coefficients and by the derivative of the nonlinearity at the unstable equilibrium. Existence of waves for the exact integro-differential equation is proved in [16] under some conditions on the integral kernel. Approximate equations are considered in [1], [8].…”