STOCHASTIC ANALYSIS FOR THE DESCRIPTION AND SYNTHESIS OF PREDATOR–PREY SYSTEMS

Abstract

Abstract In this paper, a stochastic analysis approach for predator–prey systems modeling is developed. The states of the system are assumed to have a natural probabilistic variation. Elements of queueing theory are used to describe these variations and to obtain both the transient and steady-state results for the system. The predator is considered analogous to a service facility and the prey as customers to be served. The Holling disk equation and mantid–fly experiments are analyzed by this approach. The method provides a framework for a straightforward synthesis of the system components and is readily generalized for multiple predator systems. Furthermore, hunger and other behavioral aspects can be easily incorporated into the mathematical analysis.