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.
|Number of pages||16|
|Journal||Nonlinear Analysis: Theory, Methods and Applications|
|Publication status||Published - Dec 2011|
- Lotka-Volterra model
- stochastic boundedness
- Lyapunov exponent
- variation-of-constants formula