A regime switching model for species subject to environmental noises and additive Allee effect

• Published in: Physica A Vol. 527; p. 121300
• Main Authors: Xu, Junyan, Zhang, Tonghua, Han, Maoan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2019
• Subjects: Allee effect; Ergodicity; Positive recurrence; Regime switching; Stochastic model; Survival analysis; Positive recurrence; Survival analysis; Stochastic model; Ergodicity; Regime switching; Allee effect
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2019.121300

Taking into account the environmental noises and Allee effect, we develop a regime switching model for a single species, and then we consider dynamics of species population, such as persistence, ergodicity and global attractivity. More precisely, firstly we prove the global existence of the positive solution, and then study the extinction of species, non-persistence in mean, persistence in mean and stochastic permanence. It is followed by the study of positive recurrence, ergodicity and the global attractivity. Finally, we conclude our study by a numerical example and discussions. •We developed a regime switching model for a single species.•We studied the dynamics of species subject to environmental noises and Allee effect.•We showed the extinction, persistence, and stochastic permanence of species.•We showed the positive recurrence and ergodicity of the solution.•We also showed the global attractivity of the positive solution.