This paper considers competitive Lotka-Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) We discuss the uniform boundedness of $p$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 explicit solution for 1-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|
- variation-of-constants formula
- Lotka–Volterra model
- stochastic boundedness
- Lyapunov exponent