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On hybrid competitive Lotka-Volterra ecosystems. (English) Zbl 1238.34059
Summary: We are concerned with competitive Lotka-Volterra model in random environments. It uses regime-switching diffusion to model the dynamic of population sizes of n different species in a ecosystem subject to the random changes of the external environment. We show that the positive solution of the associated stochastic differential equation does not explode in finite time with probability 1. Moreover, we demonstrate that the solution is stochastically bounded, continuous, and has finite moments. Furthermore, we obtain certain asymptotic results regarding large time behavior and present some numerical experimental results.
MSC:
34C11Qualitative theory of solutions of ODE: growth, boundedness
60J60Diffusion processes
60J05Discrete-time Markov processes on general state spaces
92D40Ecology
34D05Asymptotic stability of ODE
34F05ODE with randomness