Spatiotemporal dynamics and Turing patterns in an eco-epidemiological model with cannibalism

Abstract

In this work, we have studied the spatiotemporal dynamics and pattern formation in an eco-epidemiological model with cannibalism, which are not explored in the existing literature. Cannibalism is a process of killing and consuming the full or a part of an individual of the same species (conspecifics). A cannibalistic reaction–diffusion system is proposed and analyzed. In order to observe the change in system stability, we have investigated local and global asymptotic stability for the constant positive steady state. The existence of Hopf bifurcation and Turing instability are proved to understand the change in the system dynamics and to observe the species movement. Numerical simulation is performed to observe spatiotemporal dynamics and formation of Turing patterns. The existence of Hopf bifurcation is verified numerically in the spatiotemporal system It is observed that cannibalism stabilizes the temporal system, which is shown by bifurcation diagrams, phase portraits and time-series plots. Moreover, its increased cost promotes the occurrence of Turing patterns in the spatiotemporal system (i.e., checked numerically that for an increased cost of cannibalism, Turing instability holds). The movement of prey population also plays an important role in forming Turing patterns, as a significant change in movement results in various types of interesting two-dimensional Turing patterns such as hot-spot, stripe and labyrinth patterns. We see that both predator species show the same species distribution arrangements under cannibalistic pressure. Hence cannibalism can be seen as an essential factor for the significant change in spatiotemporal dynamics and species distribution arrangement.

Keywords

• Cannibalism
• Local stability
• Global stability
• Hopf bifurcation
• Turing instability
• Turing patterns