A stochastic model for predator-prey systems: basic properties, stability and computer simulation

✍ Scribed by M. Abundo

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 840 KB
• Volume: 29
• Category: Article
• ISSN: 0303-6812
• DOI: 10.1007/bf00164048

✦ Synopsis

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.