Existence of wave front solutions and estimates of wave speed for a competition-diffusion system
Nonlinear Analysis: Theory, Methods & Applications
A non-local delayed and diffusive predator—prey model
Nonlinear Analysis: Real World Applications
Convergence of solutions of reaction-diffusion systems with time delays
Nonlinear Analysis: Theory, Methods & Applications
Existence of travelling waves with their minimal speed for a diffusing Lotka-Volterra system
Nonlinear Analysis: Real World Applications
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In this paper, we are concerned with a two-competition model described by a reaction-diffusion system with nonlocal delays which account for the drift of individuals to their present position from their possible positions at previous times. By using the iterative technique recently developed in Wang et al. (2006) [14], the sufficient conditions are established for the existence of travelling wave solutions connecting the semi-trivial steady state to the coexistence steady state of the considered system. When the domain is bounded, we investigate the global attractivity of the coexistence steady state of the system under homogeneous Neumann boundary conditions as well. The approach used is the upper-lower solutions and monotone iteration technique.