A stochastic model for predator-prey systems: basic properties, stability and computer simulation.
A simple stochastic description of a model of a predator-prey system is given. The evolution of the system is described by means of Itô's stochastic differential equations (SDEs), which are the natural stochastic generalization of the Lotka-Volterra deterministic differential equations. Since these SDEs do not satisfy the usual conditions for the existence and uniqueness of the solution, we state a theorem of existence; moreover we study the stability of the equilibrium point and perform a computer simulation to study the behaviour of the trajectories of solutions with given initial data and to estimate first and second moments.
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Dipartimento di Matematica, II Universitá di Roma Tor Vergata, Italy.
D000818:Animals; D003198:Computer Simulation; D008433:Mathematics; D008954:Models, Biological; D015233:Models, Statistical; D011235:Predatory Behavior; D013269:Stochastic Processes