We have considered in this paper a very general predator-prey system of the Holling type with selective harvesting and where both of the species follow logistic evolution. Along with the conditions of life, the uniform limits of the structure have been studied. In addition, the criteria for local stability of different equilibrium points were obtained and the global stability of the system was discussed, considering the appropriate Lyapunov function. After that, we studied the optimal harvesting strategy for the scheme using the Pontryagin Maximal Theory. Ultimately, some numerical examples have demonstrated the problem. Finally, with the aid of a numerical illustration, we discussed the problem by using arbitrary feasible parametric values and by using MATLAB, we observed from the stability diagram (Fig. 1) and phase portrait (Fig. 2) that the steady state value of the Prey population increases as the p values decrease. This is quite a positive outcome for the organisms' ecological survival. By integrating time delay and stochasticity into the framework, our model can be expanded.
Author (s) Details
Dipankar Sadhukhan
Department of Mathematics,
Haldia Government College, Haldia-721657, W.B., India.
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