The aim of this paper is to study the dynamics of fishery resource with reserve area in the presence of bird predator. The aquatic region under investigation is divided into two zones: one free for fishing and another restricted for any kind of fishery. The criteria of biological and bionomic equilibrium of system are established. The points of local stability, global stability, and instability are obtained for the proposed model. An optimal harvesting policy is established using Pontryagin’s maximum principle. At last the theoretical results obtained are illustrated with the help of numerical simulation.

Due to overexploitation of renewable resources, we have observed that some species are already extinct. So, the time demands conservation, reproduction and optimal utilization of these resources and the study of such problems. In this paper, a delayed stage-structured self-dependent two compartment (compartment-I contains immature fishes and compartment-II contains mature fishes) commercial fishery model with impulsive harvesting is proposed and analyzed mathematically as well as numerically. The aim is to manage the fishery resource system and that to extract maximum profit without the species become extinct. The proposed system is proved to have positive periodic solutions which are bounded, locally stable and permanent with certain conditions. Then by using optimal impulsive harvesting theory, the optimal harvesting time and optimal harvesting level have been obtained. At last, numerical simulation has been done to support the analytic results, along with comparative plots drawn for different values of harvesting effort E, maturation delay τ and impulsive period T .

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The aim of this paper is to study a stage-structured pest management model with mixed type of functional response i.e., Holling type-I and Beddington-DeAngelis functional response with impulsive biological control. Stage structuring is proposed due to the fact that almost all the pests in their life pass through two stages namely, immature larva and mature adult. It is assumed that immature susceptible pests and exposed pests are attacked by a natural enemy and susceptible pests (immature and mature) are contacted by infected pests which make them exposed. Infected pests and natural enemies are infused impulsively after fixed intervals. All positive solutions are proved to be uniformly ultimately bounded. The stability analysis of pest extinction periodic solution, as well as the permanence of system, are obtained by making use of floquet's theory, small amplitude perturbation technique, and comparison theorem. The results obtained provide certain dependable theoretical findings for effective pest management. At last, theoretical findings are confirmed by means of numerical simulation.Mathematics subject classification (2010): 92D25, 34C11.

The aim of the present work is to study the dynamics of stage-structured pest control model including biological control, i.e. by releasing of natural enemies and infected pests periodically. It is assumed that only immature susceptible pests are attacked by natural enemies admitting Beddington DeAngelis functional response and mature susceptible pests are contacted by infected pests with bilinear incidence rate and become exposed. The sufficient condition for local stability of pest extinction periodic solution is derived by making use of Floquet’s theory and small amplitude perturbation technique. The global attractivity of pest extinction periodic solution is also established by applying comparison principle of impulsive differential equations.