Global Stability of Traveling Wave Fronts for a Population Dynamics Model with Quiescent Stage and Delay

TL;DR

This paper proves the global exponential stability of traveling wave fronts in a population dynamics model that includes a quiescent stage and delay, using comparison principles and weighted energy methods.

Contribution

It introduces a novel stability analysis for population models with delay and quiescent stages, extending existing results to a broader class of models.

Findings

Established comparison principle for the model

Proved global exponential stability of traveling wave fronts

Applied weighted energy method under quasi-monotonicity conditions

Abstract

This paper is concerned with the globally exponential stability of traveling wave fronts for a class of population dynamics model with quiescent stage and delay. First, we establish the comparison principle of solutions for the population dynamics model. Then, by the weighted energy method combining comparison principle, the globally exponential stability of traveling wave fronts of the population dynamics model under the quasi-monotonicity conditions is established.