Dynamical behaviour of an intraguild predator–prey model with prey refuge and hunting cooperation

ABSTRACT

An intraguild predator–prey model including prey refuge and hunting cooperation is investigated in this paper. First, for the corresponding ordinary differential equation model, the existence and stability of all equilibria are given, and the existence of Hopf bifurcation, direction and stability of bifurcating periodic solutions are investigated. Then, for partial differential equation model, the diffusion-driven Turing instability is obtained. What is more, the existence and non-existence of the non-constant positive steady state of the reaction–diffusion model are established by the Leray–Schauder degree theory and some priori estimates. Next, some numerical simulations are performed to support analytical results. The results showed that prey refuge can change the stability of model and even have a stabilizing effect on this model, meanwhile the hunting cooperation can make such model without diffusion unstable, but make such model with diffusion stable. Lastly, a brief conclusion is concluded in the last section.

KEYWORDS:

• Intraguild predation
• prey refuge
• hunting cooperation
• Leray–Schauder degree theory

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34D20
• 35B35
• 92B05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant Nos. 12161054, 11661050 and 11861044), the National Natural Science Foundation of Gansu Province (Grant No. 20JR10RA156), the Doctoral Foundation of Lanzhou University of Technology and the HongLiu First-class Disciplines Development Program of Lanzhou University of Technology.