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Competitive Lotka-Volterra population dynamics with jumps

Bao, Jianhai and Mao, Xuerong and Yin, George and Yuan, Chenggui (2011) Competitive Lotka-Volterra population dynamics with jumps. Nonlinear Analysis: Theory, Methods and Applications, 74 (17). pp. 6601-6616. ISSN 0362-546X

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Abstract

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.