The Study of a Predator‐Prey Model with Fear Effect Based on State‐Dependent Harvesting Strategy

Abstract

In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system without harvest, it is shown that the level of fear may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order- q ( q ≥ 1 ) periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order- q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB.

Complex dynamics of two prey–predator harvesting models with prey refuge and interval‐valued imprecise parameters

“…In the modeling process, these short-term disturbances are often regarded as pulses. Thus, impulsive differential equations (IDEs) provide a natural and effective description in modelling such processes, such as integrated pest management [41][42][43], prey-predator system [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59], competitive system [60][61][62]. In prey-predator system, the human interventions can be divided into prey-dependent [37,41-43, 47, 48, 51-57], predator-dependent [36,37] and ratio-dependent [63] and prey-predator hybrid-dependent [38,39,64,65].…”

The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

“…This condition involves humans, which need other organisms for their food. Harvesting generally occurs in forestry and fishery [13][14][15]. By assuming both prey and predator are proportionally harvested, we acquire…”

A systematic study of autonomous and nonautonomous predator–prey models for the combined effects of fear, refuge, cooperation and harvesting

“…Further, they have seen the impact of stochasticity on the survival as well as extinction of species in the ecological system. In [ 47 ], authors have explored the dynamics of a predator–prey system with fear effect based state-dependent harvesting. Mondal et al [ 48 ] explored different dynamical features of an imprecise predator–prey system with fear effect and nonlinear harvesting of predator in an uncertain environment.…”