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Dynamics of N-Species Cooperation Models with Feedback Controls and Continuous Delays

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Abstract

This paper studies N-species Lotka–Volterra cooperation models with feedback controls and continuous delays. Several conditions for the global attractiveness, permanence and periodic solution of the model are obtained by applying the integral inequality techniques, comparison principle and Lyapunov–Razumikhin method. Finally, a numerical example is also carried out to validate the feasibility and practicability of our proposed results.

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Acknowledgements

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Funding

This research is supported by the National Natural Science Foundation of Xinjiang (Grant No. 2021D01C067), the Open Project of Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region (Grant No. 2022D04045).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830017, People’s Republic of China

    Zhao Jiang, Ahmadjan Muhammadhaji & Cheng Hu

  2. The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi, 830017, People’s Republic of China

    Zhao Jiang & Ahmadjan Muhammadhaji

  3. College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, 830017, People’s Republic of China

    Zhidong Teng

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  1. Zhao Jiang
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  2. Ahmadjan Muhammadhaji
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  3. Cheng Hu
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Correspondence to Ahmadjan Muhammadhaji.

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Jiang, Z., Muhammadhaji, A., Hu, C. et al. Dynamics of N-Species Cooperation Models with Feedback Controls and Continuous Delays. Qual. Theory Dyn. Syst. 22, 41 (2023). https://doi.org/10.1007/s12346-023-00742-x

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