Dynamical behavior of a delayed prey-predator-scavenger system with fear effect and linear harvesting. (English) Zbl 1476.92038
Summary: In this paper, we propose a delayed prey-predator-scavenger system with fear effect and linear harvesting. First, we discuss the existence and stability of all possible equilibria. Next, we investigate the existence of Hopf bifurcation of the delayed system by regarding the gestation period of the scavenger as a bifurcation parameter. Furthermore, we obtain the direction of Hopf bifurcation and the stability of bifurcating periodic solutions by using the normal form theory and the central manifold theorem. In addition, we give the optimal harvesting strategy of the delayed system based on Pontryagin’s maximum principle with delay. Finally, some numerical simulations are carried out to verify our theoretical results.
MSC:
| 92D25 | Population dynamics (general) |
| 34D20 | Stability of solutions to ordinary differential equations |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
| 49K21 | Optimality conditions for problems involving relations other than differential equations |
Keywords:
prey-predator-scavenger; fear effect; time delay; Hopf bifurcation; optimal harvesting policyReferences:
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