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Dynamical behavior of Lotka-Volterra competition systems: non-autonomous bistable case and the effect of telegraph noise. (English) Zbl 1089.34047
The authors consider the asymptotic behaviour of solutions to a Lotka-Volterra system of two equations with deterministic or random parameters, a model of two competing populations in temporally varying deterministic or random environment. The random environment is determined by a stationary Markov process with two states and all parameters of the system can take only two values depending on the state of the Markov process.

MSC:
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92D25 Population dynamics (general)
34D05 Asymptotic properties of solutions to ordinary differential equations
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