Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 74, Issue 17, Pages 6601-6616Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2011.06.043
Keywords
Lotka-Volterra model; Jumps; Stochastic boundedness; Lyapunov exponent; Variation-of-constants formula; Extinction
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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. (C) 2011 Elsevier Ltd. All rights reserved.
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