Modelling the prudent predation in predator–prey interactions

Abstract

Prudent predators may evolve a strategy of prudent feed at a suitable rate, which is detrimental to their survival, but would not overexploit the prey thus is beneficial to the sustainability of resources. In this paper, by introducing a prey-dependent predation rate function, a two prey and one predator system with prudent predation is established, and the dynamics of the system as well as its subsystems are investigated. The existence and stability of the equilibrium are analyzed and the occurrence of Hopf bifurcation is studied. Numerical simulations are carried out to verify the analytical results and expand the theoretical analyses: (i) In the subsystems, it is possible to have multiple Hopf bifurcation points and prudence acts as a stabilizing factor; (ii) Suitable level of prudence will benefit the predator while sustaining the prey; (iii) Prudent predation can stabilize the system from chaos, which means chaotic dynamics can be controlled by the prudent predation. These results may reveal the important role of predator initiative in predator–prey interactions and enrich the dynamics of predator–prey system.