A stochastic model for predator-prey systems: basic properties, stability and computer simulation
- 1 June 1991
- journal article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 29 (6) , 495-511
- https://doi.org/10.1007/bf00164048
Abstract
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.Keywords
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