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A novel method for analyzing the stability of periodic solution of impulsive state feedback model

Author

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  • Sun, Mingjing
  • Liu, Yinli
  • Liu, Sujuan
  • Hu, Zuoliang
  • Chen, Lansun

Abstract

The complex dynamics on the single population model with impulsively unilateral diffusion between two patches was studied in a theoretical way. The existence, uniqueness and stability of an order-1 periodic solution was investigated for state-dependent impulsively differential equations. The sufficient conditions for the existence and stability of positive periodic solution were obtained using the Poincare map by comparison with the analysis for limit cycles of continuous systems, which was different from the analogue of Poincare criterion. Meanwhile, the uniqueness of periodic solution was proofed by the monotone of successor function.

Suggested Citation

  • Sun, Mingjing & Liu, Yinli & Liu, Sujuan & Hu, Zuoliang & Chen, Lansun, 2016. "A novel method for analyzing the stability of periodic solution of impulsive state feedback model," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 425-434.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:425-434
    DOI: 10.1016/j.amc.2015.09.093
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    Citations

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    Cited by:

    1. Jiang, Fangfang & Sun, Jitao, 2016. "On the existence of discontinuous periodic solutions for a class of Liénard systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 259-265.
    2. Xinmiao An & Xiaomin Wang & Boyu Zhang, 2020. "Bimatrix Replicator Dynamics with Periodic Impulses," Dynamic Games and Applications, Springer, vol. 10(3), pages 676-694, September.
    3. Liu, Qiong & Zhang, Meng & Chen, Lansun, 2019. "State feedback impulsive therapy to SIS model of animal infectious diseases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 222-232.
    4. Zhang, Meng & Zhao, Yi & Chen, Lansun & Li, Zeyu, 2020. "State feedback impulsive modeling and dynamic analysis of ecological balance in aquaculture water with nutritional utilization rate," Applied Mathematics and Computation, Elsevier, vol. 373(C).

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