Models in Ecology

In this paper, we have considered a discrete prey–predator model with square-root functional response and optimal harvesting policy. This type of functional response is used to study the dynamics o...

Stability and bifurcation analysis of a discrete prey–predator model with square-root functional response and optimal harvesting

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

In this paper, we have considered a discrete-time predator–prey model with sigmoid functional response and Allee effect. We have discussed the conditions of existence of the feasible fixed point. The stability criterion of the fixed point carried out algebraically. Analytically we have shown that the system undergoes flip and Neimark–Sacker bifurcations. We also analyzed Neimark–Sacker bifurcation by center manifold theorem taking discretization factor(generation gap) as a bifurcation parameter. Under a parametric condition, all the bifurcation phenomena and chaotic features have been justified numerically. Finally, we use the hybrid control strategy to control flip and Neimark–Sacker bifurcations.

Stability and bifurcation analysis of a discrete prey–predator model with sigmoid functional response and Allee effect

Unraveling the combined actions of a Holling type III predator–prey model incorporating Allee response and memory effects

In this paper we have analyzed a discrete prey-predator model with ratio dependent functional response and linear harvesting rate in terms of the predator species. Algebraically we have discussed the existence of fixed points, their feasibility and stability. Then Neimark-Sacker bifurcation and chaos analysis of the model have been studied algebraically with respect to the hervesting coefficient. By numerical simulation theoretical results have been justied. Finally an idea of chaos control have been proposed.

Prabir Chakraborty

Papers

Stability and bifurcation analysis of a discrete prey–predator model with square-root functional response and optimal harvesting

Stability and bifurcation analysis of a discrete prey–predator model with sigmoid functional response and Allee effect

Stability and bifurcation analysis of a ratio dependent discrete prey-predator model with linear harvesting