Competitive Lotka–Volterra population dynamics with jumps

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Bao, Jianhai and Mao, Xuerong and Yin, Geroge 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 (https://doi.org/10.1016/j.na.2011.06.043)

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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.

ORCID iDs

Bao, Jianhai, Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864, Yin, Geroge and Yuan, Chenggui;
CORE (COnnecting REpositories)