title: On stochastic Gilpin-Ayala population model with Markovian switching.
abstract: In this paper, we analyze a stochastic Gilpin-Ayala population model with Markovian switching and white noise. The Gilpin-Ayala parameter is also allowed to switch. We establish the global stability of the trivial equilibrium state of the model. Verifiable sufficient conditions which guarantee the extinction and persistence are provided. Furthermore, we show the existence of a stationary distribution. The analytical results are illustrated by computer simulations.
authors: Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Sciences and Techniques, B.P. 416 Tangier Principal, Tangier, Morocco.
authors: Adel
authors: A
authors: Settati
authors: Laboratory of Computer Sciences and Modeling, Department of Mathematics, Faculty of Sciences Dhar-Mehraz, B.P. 1796 Atlas, Fez, Morocco. Electronic address: lahrouzadil@gmail.com.
authors: Aadil
authors: A
authors: Lahrouz
mesh_terms: D008390:Markov Chains; D008954:Models, Biological; D011157:Population Dynamics; D013269:Stochastic Processes
keywords: Markovian switching; Persistence; Stability; Stationary distribution