Complex dynamics of a predator–prey model with opportunistic predator and weak Allee effect in prey

ABSTRACT

In this work, we first modify a Lotka–Volterra predator–prey system to incorporate an opportunistic predator and weak Allee effect in prey. The prey will be extinct if the combined effect of hunting and other food resources of predator is large. Otherwise, the dynamic behaviour of the system is extremely rich. A series of bifurcations such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation can happen. The validity of the theoretical results are supported with numerical simulations.

KEYWORDS:

• Opportunistic predator
• Allee effect
• predator–prey
• Hopf bifurcation
• Bogdanov–Takens bifurcation

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34C23
• 34D20
• 92D40

Disclosure statement

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

Additional information

Funding

This work was supported partially by the Natural Science Foundation of Fujian Province [2020J01499] and NSERC of Canada [RGPIN-2019-05892].