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Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model

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  • Morten Brøns
  • Mathieu Desroches
  • Martin Krupa

Abstract

In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a "weak return" mechanism, characterized by a small change in one of the variables, determines the features of the mixed-mode oscillations. Period-doubling and saddle-node bifurcations lead to closed families (called isolas ) of periodic solutions in a bifurcation corresponding to a singular Hopf bifurcation.

Suggested Citation

  • Morten Brøns & Mathieu Desroches & Martin Krupa, 2015. "Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model," Mathematical Population Studies, Taylor & Francis Journals, vol. 22(2), pages 71-79, June.
    • Handle: RePEc:taf:mpopst:v:22:y:2015:i:2:p:71-79
    DOI: 10.1080/08898480.2014.925344
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    References listed on IDEAS

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    1. Brøns, Morten & Kaasen, Rune, 2010. "Canards and mixed-mode oscillations in a forest pest model," Theoretical Population Biology, Elsevier, vol. 77(4), pages 238-242.
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    Cited by:

    1. Wen, Zihao & Li, Zhijun & Li, Xiang, 2019. "Bursting oscillations and bifurcation mechanism in memristor-based Shimizu–Morioka system with two time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 58-70.
    2. Feibiao Zhan & Yingteng Zhang & Jian Song & Shenquan Liu, 2023. "Canard Mechanism and Rhythm Dynamics of Neuron Models," Mathematics, MDPI, vol. 11(13), pages 1-22, June.

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    2. Feibiao Zhan & Yingteng Zhang & Jian Song & Shenquan Liu, 2023. "Canard Mechanism and Rhythm Dynamics of Neuron Models," Mathematics, MDPI, vol. 11(13), pages 1-22, June.
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    4. Rinaldi, Sergio, 2012. "Recurrent and synchronous insect pest outbreaks in forests," Theoretical Population Biology, Elsevier, vol. 81(1), pages 1-8.

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