Stochastic delay foraging arena predator–prey system with Markov switching. Issue 2 (3rd March 2020)

• Record Type: Journal Article
• Authors: Cai, Yongmei; Cai, Siyang; Mao, Xuerong
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 2(2020)
• Page Start: 191
• Page End: 212
• Publication Date: 2020-03-03
• Subjects: Stochastic predator–prey model -- Brownian motion -- Markov chain -- time delay -- ultimate boundedness; 37A50 -- 76M35 -- 92D25; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1679645
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.