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Abstract: This paper describes a prey–predator model with stage structure for predator and selective harvesting effort on predator population. The Holling type II functional response function is taken into consideration. All the equilibria of the proposed system are determined and the behavior of the system is investigated near them. Local stability of the system is analyzed. Geometric approach is used to derive the sufficient conditions for global stability of the system. The occurrence of Hopf bifurcation of the model system in the neighborhood of the co-existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter. Fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. Pontryagin’s maximum principle is used to characterize the optimal control. The optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. [Copyright &y& Elsevier]

Abstract: This paper describes a prey–predator fishery model with stage structure for prey. The adult prey and predator populations are harvested in the proposed system. The dynamic behavior of the model system is discussed. It is observed that singularity induced bifurcation phenomenon is appeared when variation of the economic interest of harvesting is taken into account. We have incorporated state feedback controller to stabilize the model system in the case of positive economic interest. Fishing effort used to harvest the adult prey and predator populations is used as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. Pontryagin’s maximum principle is used to characterize the optimal control. The optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a delay differential equation model for the interaction between two species, the adult members of which are in competition, with stage-structure and harvesting of the mature and immature members of each species. The maturation delay for each species is modelled as a distribution, to allow for the possibility that individuals may take a different amount of time to mature. General birth and death rate functions are used. We find that the dynamics of the model depends largely on the birth and death functions, which depend on the total number of adults. We study the dynamics of our model analytically and we present results on the positivity and boundedness of the solutions, and global stability results are established for each equilibrium. [Copyright &y& Elsevier]