Global stability of traveling wave fronts for a population dynamics model with quiescent stage and delay

Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay

This paper is concerned with the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay. Under bistable assumption, we construct various pairs of superand subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing trav...

Existence of Traveling Fronts in a Food-Limited Population Model with Spatiotemporal Delay

Exponential Stability of Traveling Fronts for a 2d Lattice Delayed Differential Equation with Global Interaction

The purpose of this paper is to study traveling wave fronts of a two-dimensional (2D) lattice delayed differential equation with global interaction. Applying the comparison principle combined with the technical weighted-energy method, we prove that any given traveling wave front with large speed is time-asymptotically stable when the initial perturbation around the wave front need decay to zero...

Existence and Stability of Traveling Wave Solutions for a Population Genetic Model via Singular Perturbations

Using singular perturbation methods, the existence and stability of traveling wave solutions for a density-dependent selection migration model in population genetics is proved. Single locus and two alleles are assumed, and it is also assumed that the fitnesses of the heterozygotes in the population are close to but below those of the homozygotes. Unlike previous models, this paper does not assu...

Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay

A delayed Lotka–Volterra type predator–prey model with stage structure for predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to prey. By analyzing characteristic equations and...