A discrete-time dynamical model of prey and stage-structured predator with juvenile hunting incorporating negative effects of prey refuge

TL;DR

This paper develops a discrete-time predator-prey model incorporating prey refuge, juvenile hunting, and prey counter-attack, analyzing stability, bifurcations, and parameter effects through theoretical and numerical methods.

Contribution

It introduces a novel discrete-time model with prey refuge and juvenile hunting, providing comprehensive stability and bifurcation analysis.

Findings

Existence and stability conditions for all fixed points

Identification of Neimark-Sacker and period-doubling bifurcations

Numerical validation of theoretical results

Abstract

This paper examines a discrete predator-prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator species. Furthermore, juvenile hunting as well as prey counter-attack are also considered. This paper provides a comprehensive analysis of the existence and stability conditions pertaining to all possible fixed points. The analytical and numerical investigation into the occurrence of different bifurcations, such as the Neimark-Sacker bifurcation and period-doubling bifurcation, in relation to various parameters is discussed. The impact of the parameters reflecting prey growth and prey refuge is thoroughly addressed. Numerous numerical simulations are presented in order to validate the theoretical findings.