Influence of predator standby capacity, harvesting and noise on a two patchy aquatic delayed eco system with migration of prey

In this article, we analyse the dynamical behaviour of a prey predator fishery model. The model is studied and analysed on the basis of harvesting of prey species in an environment which consists of two sectors. Mathematically, we have analysed the boundedness of the solution and the local stability of positive interior equilibrium point. The time lag in terms of delay parameter corresponds to the predator gestation period. The occurrence of Hopf-bifurcation of the proposed model is shown at the positive equilibrium point by considering delay as a bifurcation parameter. We observe that the system exhibits periodic oscillations due to an increase of the delay parameter. Furthermore, we examined the impact of noise on the model system using the Fourier transform technique. Finally, we verified our analytical findings by means of graphical illustrations. Keywords: Prey-predator, Stability, Time delay, Hopf-bifurcation, Noise, Global stability, Stochastic analysi