The deterministic and stochastic models of populations with Gompertz-type interaction (Q1068757)

The deterministic and stochastic population models for n-species populations which follow Gompertz' law have been proposed. Description of the situations where the model with Gompertz-type interaction among the species may be relevant, has been made. The stochasticity has been imposed by incorporating the random parts in the growth as well as in the interaction rates of the deterministic model. The Fokker-Planck equation corresponding to the stochastic differential equations arising in this manner has been approximately evaluated to obtain the transition probability for the stationary state.