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Competitive Lotka-Volterra population dynamics with jumps
Authors:Jianhai Bao
Institution:
  • a Department of Mathematics, Swansea University, Swansea SA2 8PP, UK
  • b Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UK
  • c Department of Mathematics, Wayne State University, Detroit, MI 48202, United States
  • 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.
    Keywords:93D05  60J60  60J05
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