Competitive Lotka-Volterra population dynamics with jumps |
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Authors: | Jianhai Bao |
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Institution: | a Department of Mathematics, Swansea University, Swansea SA2 8PP, UKb Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UKc Department of Mathematics, Wayne State University, Detroit, MI 48202, United States |
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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 that a stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) we discuss the uniform boundedness of the pth 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 an explicit solution for one-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. |
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Keywords: | 93D05 60J60 60J05 |
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