Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response

Md Golam Mortuja, Mithilesh Kumar Chaube and Santosh Kumar

Chaos, Solitons & Fractals, 2021, vol. 148, issue C

Abstract: In this work, the dynamics of a predator-prey system considering square root type functional response for prey herd behaviour and nonlinear prey harvesting has been analyzed. The conditions under which all equilibria exist as well as the stability of every equilibrium point of the system have been investigated. The proposed model conditionally posses two types of bifurcations, Hopf bifurcation, and saddle-node bifurcation. The saddle-node bifurcation has been analyzed, where the bifurcation parameter is harvesting rate. The existence of a maximum sustainable yield to ensure both populations coexist has been discussed. The results give a clear idea that, if the harvesting rate is chosen at a proper value lesser than the maximum sustainable yield then both populations will coexist and the ecological balance will be maintained. The calculation of the first Lyapunov number provides the Hopf bifurcation direction. To verify our analytical results, several numerical simulations have been carried out.

Keywords: Predator-prey system; Group defense; Nonlinear harvesting; Square root functional response; Stability analysis (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921004252

DOI: 10.1016/j.chaos.2021.111071

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