Competitive Lotka–Volterra population dynamics with jumps

• DOI: 10.1016/j.na.2011.06.043
• Publication Date: 2011-07-24T21:31:30Z
• Authors: Jianhai Bao; Xuerong Mao; Geroge Yin; Chenggui Yuan
• Keywords: Volterra equations; Dynamics

25 pages<br/>This paper considers competitive Lotka-Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) We discuss the uniform boundedness of $p$th moment with $p>0$ and reveal the sample Lyapunov exponents; (c) Using a variation-of-constants formula for a class of SDEs with jumps, we provide explicit solution for 1-dimensional competitive Lotka-Volterra population dynamics with jumps, and investigate the sample Lyapunov exponent for each component and the extinction of our $n$-dimensional model.<br/>