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Dynamical behavior of a competitive system under the influence of random disturbance and toxic substances

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Abstract

A two-species competitive system under the influence of random disturbance and toxic substances is studied theoretically and numerically. The existence of a stationary distribution, extinction, and stability of this model are considered. Our results show that both the environmental disturbance and toxic substances can destabilize biological populations. A set of sufficient conditions which guarantee that one of the species is driven to extinction while the other is stable in the mean is illustrated. Numerical simulations are also presented to illustrate the feasibility of our main results.

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Acknowledgments

This research was partially supported by grants from the National Natural Science Foundation of PR China (No. 11301207), (No. 11301112), (No. 11171081), (No. 11171056), (No. 11126219), (No. 11001032), (No. 11101183), and (No. 11226254); Project (HIT.NSRIF.2015103) by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology, Natural Science Research Project of Ordinary Universities in Jiangsu Province (No. 13KJB110002).

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai , 264209, People’s Republic of China

    Ruihua Wu, Xiaoling Zou & Ke Wang

  2. College of Science, China University of Petroleum (East China), Qingdao , 266555, People’s Republic of China

    Ruihua Wu

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  1. Ruihua Wu
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  2. Xiaoling Zou
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  3. Ke Wang
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Correspondence to Xiaoling Zou.

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Wu, R., Zou, X. & Wang, K. Dynamical behavior of a competitive system under the influence of random disturbance and toxic substances. Nonlinear Dyn 77, 1209–1222 (2014). https://doi.org/10.1007/s11071-014-1371-8

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  • DOI: https://doi.org/10.1007/s11071-014-1371-8

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