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Nonchaos-Mediated Mixed-Mode Oscillations in a Prey-Predator Model with Predator Dormancy

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Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Chaos-mediated mixed-mode oscillations were recently detected among complex oscillations supported by a prey-predator model including dormancy, a strategy to avoid extinction. Here we show that, as the carrying capacity grows, there are surprisingly wide phases of nonchaos-mediated mixed-mode oscillations that occur before the onset of chaos in the system. Nonchaos-mediated cascades display spike-adding sequences while chaos-mediated cascades show spike-doubling. In addition, we find a host of exotic periodic phases embedded in a region of control parameters dominated by chaotic oscillations of the prey-predator populations. We describe these complicated phases, show how they are interconnected, and how their complexity unfolds as control parameters change. The new nonchaos-mediated phases are stable and large, even at low carrying capacity.

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Acknowledgements

JGF was supported by a postdoctoral fellowship (SFRH/BPD/101760/2014), from the FCT, Portugal. JACG was supported by CNPq, Brazil. All phase diagrams were computed on the CESUP-UFRGS Supercomputing Center located in Porto Alegre, Brazil.

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Authors and Affiliations

  1. Instituto de Altos Estudos da Paraíba, Rua Silvino Lopes 419-2502, João Pessoa, PB, 58039-190, Brazil

    Joana G. Freire, Marcia R. Gallas & Jason A. C. Gallas

  2. Departamento de Física, Universidade Federal da Paraíba, João Pessoa, 58051-970, Brazil

    Joana G. Freire, Marcia R. Gallas & Jason A. C. Gallas

  3. Faculdade de Ciências, Instituto Dom Luiz, Universidade de Lisboa, 1749-016, Lisbon, Portugal

    Joana G. Freire

  4. Complexity Sciences Center, 9225 Collins Ave. #1208, Surfside, FL, 33154-3046, USA

    Marcia R. Gallas & Jason A. C. Gallas

Authors
  1. Joana G. Freire
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  2. Marcia R. Gallas
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  3. Jason A. C. Gallas
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Corresponding author

Correspondence to Jason A. C. Gallas .

Editor information

Editors and Affiliations

  1. Stern College for Women, Yeshiva University, New York, New York, USA

    Mark Edelman

  2. INPE/LAC, Instituto Nacional de Pesquisas Espaciai, São José dos Campos, São Paulo, Brazil

    Elbert E. N. Macau

  3. Departamento de Fisica, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain

    Miguel A. F. Sanjuan

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Freire, J.G., Gallas, M.R., Gallas, J.A.C. (2018). Nonchaos-Mediated Mixed-Mode Oscillations in a Prey-Predator Model with Predator Dormancy. In: Edelman, M., Macau, E., Sanjuan, M. (eds) Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-68109-2_6

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