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Periodicity induced by state feedback controls and driven by disparate dynamics of a herbivore–plankton model with cannibalism

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Abstract

Plankton and herbivore in aquatic ecosystems are often deeply disturbed by human exploitations in impulsive patterns. In this paper, for a herbivore–plankton interaction model with cannibalism, firstly, the complex dynamic behaviors including the number, the existence and stability of internal equilibriums, the limit and homoclinic cycles, Hopf, saddle node, Pitchfork and Bogdanov–Takens bifurcations are investigated roughly. Furthermore, multiple state feedback controls are implemented so that three order-one periodic solutions (OOPSs) and heteroclinic bifurcation driven by disparate dynamics are induced, respectively. By the method of Bendixson theorem and successor function, the existences of OOPSs are proved. Finally, for the corresponding small parameter-perturbed system, B-convergent of OOPS and homoclinic bifurcation are investigated by the variational equation and the rotated vector, respectively.

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Acknowledgements

The authors would like to appreciate the editors and the reviewers for their constructive and helpful comments. The work is supported by the National Natural Science Foundation of China (11471243, 11501409, 11671346).

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Authors and Affiliations

  1. School of Science, Tianjin Polytechnic University, Tianjin, 300387, China

    Dandan Fang, Yongzhen Pei & Yunfei Lv

  2. School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin, 300387, China

    Yongzhen Pei

  3. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China

    Lansun Chen

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  1. Dandan Fang
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  2. Yongzhen Pei
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  3. Yunfei Lv
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  4. Lansun Chen
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Correspondence to Yongzhen Pei.

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The work was supported by the National Natural Science Foundation of China (11471243).

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Fang, D., Pei, Y., Lv, Y. et al. Periodicity induced by state feedback controls and driven by disparate dynamics of a herbivore–plankton model with cannibalism. Nonlinear Dyn 90, 2657–2672 (2017). https://doi.org/10.1007/s11071-017-3829-y

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