Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species

Front dynamics in a two-species competition model driven by Lévy flights.

A number of recent studies suggest that many biological species follow a Lévy random walk in their search for food. Such a strategy has been shown to be more efficient than classical Brownian motion when resources are scarce. However, current diffusion-reaction models used to describe many ecological systems do not account for the superdiffusive spread of populations due to Lévy flights. We hav...

Global Existence of Classical Solutions to a Three-Species Predator-Prey Model with Two Prey-Taxes

Stability and Bifurcations in Delayed Three-Species Model

In this study, a system of delay differential equations arising from a three-species model with two predators feeding on a single prey is considered. It is assumed that the prey population grows logistically in the absence of predators, and both predator populations adapt a Holling type II functional response. Each response term includes a delay time, which reflects the gestation period of each...

The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population

A mathematical model describing the dynamics  of a  delayed  stage structure prey - predator  system  with  prey  refuge  is  considered.  The  existence,  uniqueness  and bounded- ness  of  the  solution  are  discussed.    All  the  feasibl e  equilibrium  points  are determined.  The   stability  analysis  of  them  are  investigated.  By  employ ing  the time delay as the bifurcation parame...

Integrated pest management with stochastic birth rate for prey species

Song and Xiang (2006) developed an impulsive differential equations model for a two-prey one-predator model with stage structure for the predator. They demonstrate the conditions on the impulsive period for which a globally asymptotically stable pest-eradication periodic solution exists, as well as conditions on the impulsive period for which the prey species is permanently maintained under an ...