Asymptotic properties of a stochastic Lotka–Volterra model with infinite delay and regime switching

• Main Authors: Qingteng Lin, Lijing Chen, Chunlan Wen, Fengying Wei
• Format: Article
• Language: English
• Published: SpringerOpen 2018-05-01
• Series: Advances in Difference Equations
• Subjects: Stochastic Lotka–Volterra model; Markovian chains; Infinite delay; Stochastically ultimate boundedness; Moment estimation
• Online Access: http://link.springer.com/article/10.1186/s13662-018-1609-8
• ISSN: 1687-1847

Abstract We investigate the long-term properties of a stochastic Lotka–Volterra model with infinite delay and Markovian chains on a finite state space. We investigate that the stochastic model admits a unique positive global solution which stays in the way of stochastically ultimate boundedness by constructing Lyapunov functions. Furthermore, the main results that the growth of the solution is slower than time under moderate condition and moment estimation in time average with the power p could be controlled are derived, which modified the known ones in recent literatures.