Stability analysis of a non-cooperative system of reaction-diffusion equations modeling two sub-populations with mixed dispersal.

Abstract

This study is concerned with the global stability of positive equilibrium (PE) solutions in a juvenile-adult structured diffusive model featuring a mixed dispersal mechanism. Under certain generic assumptions, we establish the uniqueness and global stability of the PE. Moreover, we show that these assumptions hold if either (i) the population disperses slowly, or (ii) the adults' reproduction rate is large. In particular, our findings demonstrate that a high adult reproduction rate always benefits species survival. Interestingly, with elevated juvenile maturity rates, the population can face extinction if the average death rate of adults surpasses their average reproduction rate. A key aspect of our analysis involves deriving the exact asymptotic limit of the principal spectrum point of some cooperative systems with mixed dispersals with respect to specific model parameters. In addition, we conducted numerical simulations to illustrate our theoretical results.