Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise
Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise
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DOI：
10.1016/j.jde.2014.05.029
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发表时间：
2014-09
影响因子：
2.4
通讯作者：
N. H. Dang;N. Du;G. Yin
中科院分区：
文献类型：
--
作者：
N. H. Dang;N. Du;G. Yin
本文研究了两个物种在电报噪声下的竞争型Kolmogorov系统的种群动力学，该系统被描述为一个具有两个状态的连续时间马尔可夫链。我们的主要努力是建立一个不变（或固定）的概率测度的存在。此外，在适当的条件下，证明了瞬时测度按全变差收敛于平稳测度。此外，Ω-极限集的模型中，每个物种是占主导地位的电报噪声的状态进行了详细检查。
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, theΩ-limit set of a model in which each species is dominant in a state of the telegraph noise is examined in detail.