output regulation

hopf bifurcation

predator prey

predator prey model

hboc

russian

prey system

cathode_56263

prey_74331

predator-prey model

positive equilibrium

suvorexant

refuge

prey_99067

hummingbird

moral_77014

top predator

adhd_122973

Chaos Solitons & Fractals

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.

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