Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise |
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Authors: | NH Dang NH Du G Yin |
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Institution: | 1. Department of Mathematics, Wayne State University, Detroit, MI 48202, USA;2. Department of Mathematics, Mechanics and Informatics, Hanoi National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam |
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Abstract: | This work focuses on population dynamics of two species described by Kolmogorov systems of competitive type under telegraph noise that is formulated as a continuous-time Markov chain with two states. Our main effort is on establishing the existence of an invariant (or a stationary) probability measure. In addition, the convergence in total variation of the instantaneous measure to the stationary measure is demonstrated under suitable conditions. Moreover, the Ω-limit set of a model in which each species is dominant in a state of the telegraph noise is examined in detail. |
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Keywords: | 34C12 60H10 92D25 |
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