Dichotomic Process Research Articles

TWO‐SPECIES SYSTEMS IN RANDOM ENVIRONMENT

AbstractAn exactly solvable model for two interacting species with stochastic parameters is investigated. The parameter describing the interaction is assumed to be characterized by a dichotomic Markov process. It is remarkable that in contrast to the usual oscillatory behaviour in the deterministic case the expected value of the logarithm of each population size, as a consequence of parametric stochastic perturbations, attains a stable value as time increases. check that in their absence the damping term vanishes, leading to the deterministic model of Gomatam.

A stochastic model for two interacting species

An exactly solvable stochastic model for two interacting species with a prey-predator relationship in the presence of self-interaction is investigated. The parameters describing the interactions are assumed to be represented by a dichotomic Markov process. Explicit expressions are derived for the time development of the average of the logarithm of the population size in respect of each species and their asymptotic behaviours are discussed.