The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect

Abstract

We study the dynamics of a delayed predator-prey model with double Allee effect. For the temporal model, we showed that there exists a threshold of time delay in predator-prey interactions; when time delay is below the threshold value, the positive equilibriumE∗is stable. However, when time delay is above the threshold value, the positive equilibriumE∗is unstable and period solution will emerge. For the spatiotemporal model, through numerical simulations, we show that the model dynamics exhibit rich parameter space Turing structures. The obtained results show that this system has rich dynamics; these patterns show that it is useful for a delayed predator-prey model with double Allee effect to reveal the spatial dynamics in the real model.

A switched multicontroller for an SEIADR epidemic model with monitored equilibrium points and supervised transients and vaccination costs

“…Flow diagram of the control-free model transitions [45,46]. In particular, a discrete epidemic model is investigated in [14], which possesses a unique nonnegative equilibrium to which the solutions converge, and the case of imperfect vaccination under nonlinear incidence rate is investigated in [16].…”

Qualitative Analysis of a Spatiotemporal Prey‐Predator Model with Additive Allee Effect and Fear Effect

“…Especially, introducing the Allee effect into the model makes the dynamic behavior of the model closer to reality. e spatiotemporal complexity of a delayed predator-prey model with double Allee effect was given by [11]. In [12], P. J. Pal and S. Tapan consider a system with a double Allee effect in prey population growth, which are very sensitive to parameter perturbations and position of initial conditions.…”