Effect of seasonality on the dynamics of 2 and 3 species prey-predator systems

In this paper, we have studied perturbed versions of four distinct continuous time model systems (considered by earlier authors), describing feasible ecological situations. We compare the dynamics of the original systems with those of the seasonally perturbed ones. It is found that the seasonally induced perturbations of even the weaker strength transform the stable limit cycle attractors into chaotic ones in the case of two-dimensional systems. However, strong perturbations are required to effect the same in the case of the three-dimensional ecosystems. It is found that seasonal perturbations do not destroy the chaotic attractors. The computed bifurcation diagram and the two-dimensional parameter scans suggest that the seasonal perturbations causing changes in the system parameters and deciding different dynamics are able to induce variations in the dynamical modes frequently. These results may be helpful in working out some strategies for the management of man made or natural ecosystems involving economically important species, in designing conservation efforts, and in framing management strategies for the rare and endangered species.