Dynamics of a delayed population patch model with the dispersion matrix incorporating population loss

TL;DR

This paper analyzes a delayed population patch model with dispersal and population loss, examining equilibrium stability, bifurcations, and the influence of network topology on population dynamics.

Contribution

It introduces a general delayed patch model incorporating population loss and studies stability, bifurcations, and network effects, which are novel in this context.

Findings

Unique positive equilibrium exists below a critical dispersal rate.

Stability and Hopf bifurcation depend on dispersal rate and network topology.

Network structure significantly influences bifurcation values.

Abstract

In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate is smaller than a critical value. The stability of the positive equilibrium and associated Hopf bifurcation are investigated when the dispersal rate is small or near the critical value. Moreover, we show the effect of network topology on Hopf bifurcation values for a delayed logistic population model.