Dynamical behavior of a delayed prey-predator-scavenger system with fear effect and linear harvesting
Xin-You Meng, Jie Li
Abstract
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.
Topics & Concepts
Hopf bifurcationMathematicsCenter manifoldControl theory (sociology)Stability (learning theory)Applied mathematicsBifurcationNonlinear systemPhysicsComputer scienceQuantum mechanicsMachine learningControl (management)Artificial intelligenceMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsFractional Differential Equations Solutions