Role of wind on the dynamic of stage structured predator-prey system with cannibalism

Abstract

This article presents a new mathematical model of a predator-prey ecosystem that contains biological relations such as wind flow, stage structure, and cannibalism. To perform the dynamic analysis of the system, the positivity and boundedness of the proposed system were examined, and feasible equilibrium points were found. By utilizing the linearization technique and Lyapunov functions, the local and global stability were established, respectively. All conditions for persistence were identified. By the bifurcation theory, the impacts of changing the parameters were examined. A numerical simulation was used to validate our analytical results by using MATLAB code (version R2018b). It is found that the impact of wind flow plays a major role in the dynamics of the system. When the wind flow increases, then the predators (mature and immature) become extinct, which means the effect of wind flow hinders the reduction and efficiency of predators. On the other hand, the cannibalism coefficient also affects the dynamics of the system, whereby the bistable state appears.