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.


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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