Hunting cooperation in a prey–predator model with maturation delay

ABSTRACT

We investigate the dynamics of a prey–predator model with cooperative hunting among specialist predators and maturation delay in predator growth. First, we consider a model without delay and explore the effect of hunting time on the coexistence of predator and their prey. When the hunting time is long enough and the cooperation rate among predators is weak, prey and predator species tend to coexist. Furthermore, we observe the occurrences of a series of bifurcations that depend on the cooperation rate and the hunting time. Second, we introduce a maturation delay for predator growth and analyse its impact on the system's dynamics. We find that as the delay becomes larger, predator species become more likely to go extinct, as the long maturation delay hinders the growth of the predator population. Our numerical exploration reveals that the delay causes shifts in both the bifurcation curves and bifurcation thresholds of the non-delayed system.

KEYWORDS:

• Hunting cooperation
• maturation delay
• stability
• Hopf bifurcation

AMS SUBJECT CLASSIFICATIONS:

• 34C23
• 34D20
• 92D40

Acknowledgements

The authors wish to express their gratitude to the editors and anonymous referees for helpful comments and valuable suggestion which improved the quality of this paper.

Disclosure statement

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

Additional information

Funding

This research was partially supported by JSPS KAKENHI Grant Number 19K14598 (YE).