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Fast–Slow Dynamics for Intraguild Predation Models with Evolutionary Effects

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Abstract

This work is concerned with the fast–slow dynamics for intraguild predation models with evolutionary effects. Assuming the survival pressure of the weaker predator induces evolution of it to the intraguild predator, then the system can be viewed as a singularly perturbed problem with two different time scales—predation time scale and evolution time scale. Using the geometric singular perturbation theory, we first completely analyze the limiting slow–fast dynamics of the system which involve the existence of turning points. Then, an application of the geometric singular perturbation theory gives rise to the birth of relaxation oscillations caused by the turning points and the associated delay of stability loss. From our main results, one can see that evolution enhances survival rates of inferior competitors.

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Acknowledgements

The authors would like to thank the anonymous referee’s valuable comments and suggestions which have led to an improvement of the presentation.

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Authors and Affiliations

  1. College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou, 350007, People’s Republic of China

    Jianhe Shen

  2. Department of Mathematics, National Central University, Zhongli District, Taoyuan City, 32001, Taiwan

    Cheng-Hsiung Hsu

  3. Department of Mathematics, Tamkang University, Tamsui District, New Taipei City, 25137, Taiwan

    Ting-Hui Yang

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  1. Jianhe Shen
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  2. Cheng-Hsiung Hsu
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  3. Ting-Hui Yang
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Correspondence to Cheng-Hsiung Hsu.

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Jianhe Shen: This author was partially supported by the National Natural Science Foundation of China (Grant No. 11771082). Cheng-Hsiung Hsu:This author was partially supported by the MOST (Grant No. 107-2115-M-008-009-MY3) and NCTS of Taiwan. Ting-Hui Yang: This author was partially supported by the MOST (Grant No. 106-2115-M-032 -003-MY2) and NCTS of Taiwan.

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Shen, J., Hsu, CH. & Yang, TH. Fast–Slow Dynamics for Intraguild Predation Models with Evolutionary Effects. J Dyn Diff Equat 32, 895–920 (2020). https://doi.org/10.1007/s10884-019-09744-3

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