Dynamics of Kolmogorov systems of competitive type under the telegraph noise
The authors study the dynamics of a special system of stochastic differential equations with telegraph noise and describe completely all \(\omega\)-limit sets of the solutions. Moreover, they show that the stationary distribution (if it exists) has a density and attracts all other distributions. The presented results extend important properties of this special system [see for example \textit{L. J. S. Allen}, An introduction to stochastic processes with applications to biology. Upper Saddle River, NJ: Pearson Education (2003; Zbl 1205.60001); \textit{N. H. Du, R. Kon, K. Sato} and \textit{Y. Takeuchi}, J. Comput. Appl. Math. 170, No. 2, 399--422 (2004; Zbl 1089.34047); \textit{L. J. S. Allen} and \textit{E. J. Allen}, Theor. Popul. Biol. 64, No. 4, 439--449 (2003; Zbl 1105.92023); \textit{L. Arnold, W. Horsthemke} and \textit{J. W. Stuckl}, Biom. J. 21, 451--471 (1979; Zbl 0433.92019); \textit{J. Golec} and \textit{S. Sathananthan}, Math. Comput. Modelling 38, No. 5--6, 585--593 (2003; Zbl 1052.34064); \textit{Q. Luo} and \textit{X. Mao}, J. Math. Anal. Appl. 334, No. 1, 69--84 (2007; Zbl 1113.92052)].
scientific article; zbMATH DE number 5834240
scientific article