Population dynamical behavior of Lotka-Volterra system under regime switching

@article{Li2009PopulationDB,
  title={Population dynamical behavior of Lotka-Volterra system under regime switching},
  author={Xiaoyue Li and Daqing Jiang and Xuerong Mao},
  journal={J. Computational Applied Mathematics},
  year={2009},
  volume={232},
  pages={427-448}
}
where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction. We find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Morkov chain. The limit of the average in time of the sample path of the solution is then estimated by two constants related to the… CONTINUE READING
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