Dynamics and Bifurcation Analysis of a Filippov Predator–Prey Ecosystem in a Seasonally Fluctuating Environment

Abstract

Mathematical models can assist to design and understand control strategies for limited resources in Integrated Pest Management (IPM). This paper studies the dynamical behavior of a Filippov predator–prey model with periodic forcing. Firstly, bifurcation analyses are carried out to show that the Filippov predator–prey ecosystem may have very complex dynamics, i.e. the system may have periodic, quasi-periodic, chaotic solutions, as well as period doubling bifurcations. Meanwhile, the model is analyzed theoretically and numerically to understand how resource limitation and periodic forcing affect pest population outbreaks, the intersection between the initial densities (pest and natural enemy populations) and pest control has been discussed. Furthermore, the sliding surface, sliding mode dynamics, the existence and stability of sliding periodic solution of the proposed model and its application in IPM strategy are investigated. Our results show that several hidden factors can adversely affect our control strategy in limited resource and fluctuating environment. Thus, choosing a proper threshold value ET may play a decisive role in pest control, which confirms that IPM is the optimal control strategy.