Dynamics of Holling-type II prey–predator system with a protection zone for prey

ABSTRACT

In this paper, a diffusive predator–prey model with Holling type II (Michaelis–Menten) functional response and a protection zone for prey is investigated. Dynamics and steady state solutions of the system are analyzed. We give the a priori estimates and obtain the nonexistence of nonconstant positive solution as the diffusion coefficients are large enough. Moreover, we demonstrate the existence and stability of nonconstant steady state solutions branching from constant semi-trivial solution by using bifurcation theory.

Keywords:

• Predator–prey model
• global existence
• a priori estimates
• protection zone
• bifurcation
• reaction–diffusion
• Holling-type II functional response

AMS Subject Classifications:

• Primary: 92D25
• 92D50
• Secondary: 35A01
• 35B32
• 35B45
• 35K57

Acknowledgements

The authors would like to thank the reviewers for their helpful comments and suggestions that significantly improve the initial version of this paper.

Disclosure statement

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

Additional information

Funding

This work is supported by National Natural Science Foundation of China (NSFC) [grant number 11771110].