Dynamics of harvested-predator–prey model: role of alternative resources

Abstract

In this paper, A predator-prey model with square root functional response for herd behaviour of prey incorporating predator harvesting is proposed and analysed. The predator population is provided with alternative resource. The proposed model is demonstrated in respect of theoretical as well as numerical results. The Pontryagin's maximum principle is used to characterized the optimal harvesting strategy. Bifurcation study with the variation of harvesting effort and alternative resource are done in respect of numerical simulation. Simulation results show that suitable alternative resource has the capability to prevent predator extinction risk at higher harvesting level. The proposed model and obtaining results are usable in the field of conservation of biology.

Mathematical Study on a Dynamical Predator-Prey Model with Constant Prey Harvesting and Proportional Harvesting in Predator

“…To tackle that type of situation, many researchers worked on a predator-prey system with harvesting effects (15) (16) (17) (18). Basically researchers used three types of harvesting and the classification is constant harvesting (19), proportional harvesting (20) and non-linear harvesting (21). In this paper we consider harvested predator and prey population.…”

The Effect of Alternative Resource and Refuge on the Dynamical Behavior of Food Chain Model

“…Ghosh et al [10] examined prey-predator dynamics, wherein the predator receives more food from the prey shelter. Sahoo et al [31] examined the impact of substitute resources on the dynamics of the harvested-predator-prey model. Given the aforementioned information, in order to address the consequences of alternative resources for a top predator, the researchers were driven to examine the mathematical depiction of prey refuge in a three-species dietary chain using a second kind of Holling predation rate.…”

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

“…An optimal harvesting policy is explored by Zhang et al [ 44 ], on a stage-structured two species model. Sahoo et al [ 45 ] studied the role of alternative resources on the dynamics of a harvested predator–prey system. They showed the capability of suitable alternative resources to reduce the risk of extinction of predator species if the rate of harvesting is too high.…”