Stochastic Gomatam Model of Interacting Species: Non-Equilibrium Fluctuation and Stability

The object of the article is to study the stability behaviour of the stochastic version of the Gomatam model of interacting species. The reproductive and mortality factors of the prey and predator species respectively are perturbed by coloured noises due to random environment. Using spectral density analysis we show that this system exhibits large fluctuations for high amplitude random forces. When the intraspecific interaction coefficients tend to zero along a straight line, this system exhibits abnormally large fluctuations with increasing time with a periodic background noise. We also obtain a relation between the real part of the eigen values of the interaction matrix in the deterministic environment and the stability of this system in the stochastic environment. Keywords: Prey-predator SystemColoured NoiseWhite NoiseSpectral Density FunctionFluctuationStability