Deterministic and stochastic analysis of a prey-dependent predator-prey system

This paper reports on studies of the deterministic and stochastic behaviours of a predator-prey system with prey-dependent response function. The first part of the paper deals with the deterministic analysis of uniform boundedness, permanence, stability and bifurcation. In the second part the reproductive and mortality factors of the prey and predator species are perturbed by coloured noise to simulate a random environment. Using spectral density analysis it has been shown that this system exhibits large fluctuations for high amplitude random forces. When k, the carrying capacity of prey, tends to a particular value k*, this system exhibits abnormally large fluctuations with increasing time with a periodic background noise. A comparative study of the deterministic and stochastic criteria of stability is also established.