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A discrete age-structured Bernardelli, Lewis and Leslie (BLL) population model for a single species is formulated under age dependent harvesting condition. Here, after an initial period during which the growth of the species is not much, harvesting is performed. Its rate is proportional to the available bio-mass (number of species) of different age group population and decreases with the age of the species by considering monotonic decreasing catch per unit effort parameter. The modified Leslie matrix for the present models is derived. Stability of the system is studied from the ratio of the population densities with respect to times. This kind of study is very important in population biology as to get an idea about the future biomass and sustainability of the species.

In this paper, we have considered a very general Holling type predator-prey system with selective harvesting and where both of the species follow logistic growth. The uniform boundedness of the system has been studied together with the conditions of existence. Also, we have obtained the criteria for local stability of various equilibrium points then considering suitable Lyapunov function, the global stability of the system has been discussed. After that using Pontryagin Maximal Principle, we have studied the optimal harvesting policy for the system. At the end, the problem has been illustrated through some numerical examples. Finally, we have discussed the problem with the help of a numerical example by using arbitrary feasible parametric values and using MATLAB, we observed from stability diagram (Fig. 1) and phase portrait (Fig. 2) that as the values of decreases, the steady state value of Prey population increases. This is quite good result for ecological sustainability of species. Our model may be extended by incorporating time delay and stochasticity in the system.

In this paper, both deterministic and stochastic behaviors of a general prey-predator model have been studied with Holling type-IV response function. For the deterministic model, uniform boundedness and persistence of the system have been discussed under the certain condition of the parameter. For local stability and bifurcation analysis, we arrive at the Hopf bifurcation and derived the symbolic condition for Hopf bifurcation. After that, the model has been illustrated with some numerical examples. In the second phase, the system has been perturbed by independent Gaussian white noises for the stochastic environment and the stability of the system have been studied by statistical linearization technique. Finally, a comparison has been made between the stability conditions in deterministic and stochastic cases.