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Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 3240-3251. doi: 10.3934/mbe.2020184
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Research article

Extinction and stationary distribution of a competition system with distributed delays and higher order coupled noises

  • Department of Mathematics, Hubei Minzu University, Enshi, Hubei 445000, China

  • 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.

    Citation: Jing Hu, Zhijun Liu, Lianwen Wang, Ronghua Tan. Extinction and stationary distribution of a competition system with distributed delays and higher order coupled noises[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3240-3251. doi: 10.3934/mbe.2020184

    Related Papers:

  • 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.
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    © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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