Modeling and dynamical analysis of a triple delayed prey–predator–scavenger system with Lévy jumps

Abstract

In this paper, a hybrid triple delayed prey–predator–scavenger system with commercial harvesting and Lévy jumps is established, where both maturation delay for prey population and gestation delays for predator and scavenger population are considered. For deterministic system, positivity and uniform permanence of solution are discussed. Local stability analysis of deterministic system around interior equilibrium is investigated due to variations of triple time delays. For stochastic system without time delay, sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed. For stochastic system with triple time delays, existence and uniqueness of global positive solution are studied. By constructing appropriate Lyapunov functions, asymptotic behavior of the hybrid stochastic system with triple time delays and Lévy jumps is discussed. Numerical simulations are supported to illustrate theoretical results.