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Extinction in Two‐Species Nonlinear Discrete Competitive System

Author

Listed:
  • Liqiong Pu
  • Xiangdong Xie
  • Fengde Chen
  • Zhanshuai Miao

Abstract

We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov‐type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.

Suggested Citation

  • Liqiong Pu & Xiangdong Xie & Fengde Chen & Zhanshuai Miao, 2016. "Extinction in Two‐Species Nonlinear Discrete Competitive System," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:2806405
    DOI: 10.1155/2016/2806405
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    References listed on IDEAS

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    1. Qinglong Wang & Zhijun Liu, 2013. "Uniformly Asymptotic Stability of Positive Almost Periodic Solutions for a Discrete Competitive System," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, May.
    2. Ronghua Tan & Zuxiong Li & Qinglong Wang & Zhijun Liu, 2014. "Positive Periodic Solutions of a Periodic Discrete Competitive System Subject to Feedback Controls," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Chao Liu & Yuanke Li, 2014. "Global Stability Analysis of a Nonautonomous Stage‐Structured Competitive System with Toxic Effect and Double Maturation Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Ronghua Tan & Zuxiong Li & Qinglong Wang & Zhijun Liu, 2014. "Positive Periodic Solutions of a Periodic Discrete Competitive System Subject to Feedback Controls," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, June.
    5. Qinglong Wang & Zhijun Liu & Zuxiong Li, 2013. "Positive Almost Periodic Solutions for a Discrete Competitive System Subject to Feedback Controls," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. Qinglong Wang & Zhijun Liu, 2013. "Uniformly Asymptotic Stability of Positive Almost Periodic Solutions for a Discrete Competitive System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    7. Chao Liu & Yuanke Li, 2014. "Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-15, October.
    8. Qinglong Wang & Zhijun Liu & Zuxiong Li, 2013. "Positive Almost Periodic Solutions for a Discrete Competitive System Subject to Feedback Controls," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-14, November.
    9. Chen, Fengde & Xie, Xiangdong & Miao, Zhanshuai & Pu, Liqiong, 2016. "Extinction in two species nonautonomous nonlinear competitive system," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 119-124.
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