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Competitive Lotka-Volterra population dynamics with jumps. (English) Zbl 1228.93112
Summary: 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 $p$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 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.
##### MSC:
 93E03 General theory of stochastic systems 60J60 Diffusion processes 60J05 Discrete-time Markov processes on general state spaces 60H10 Stochastic ordinary differential equations
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