Open AccessExtinction and stationary distribution of a competition system with distributed delays and higher order coupled noises
Author(s) -
Jing Hu,
Zhijun Liu,
Lianwen Wang,
Renxiang Tan
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020184
Subject(s) - extinction (optical mineralogy) , stationary distribution , competition (biology) , nonlinear system , saturation (graph theory) , coupling (piping) , distribution (mathematics) , noise (video) , control theory (sociology) , order (exchange) , competition model , mathematics , physics , statistical physics , mathematical analysis , computer science , biology , engineering , statistics , ecology , combinatorics , economics , optics , quantum mechanics , artificial intelligence , markov chain , image (mathematics) , microeconomics , profit (economics) , control (management) , mechanical engineering , finance
A stochastic two-species competition system with saturation effect and distributed delays is formulated, in which two coupling noise sources are incorporated and every noise source has effect on two species' intrinsic growth rates in nonlinear form. By transforming the two-dimensional system with weak kernel into an equivalent four-dimensional system, sufficient conditions for extinction of two species and the existence of a stationary distribution of the positive solutions to the system are obtained. Our main results show that the two coupling noises play a significant role on the long time behavior of system.