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

  • Joana G. Freire
  • Marcia R. Gallas
  • Jason A. C. Gallas
Part of the Understanding Complex Systems book series (UCS)


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.



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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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Joana G. Freire
    • 1
    • 2
    • 3
  • Marcia R. Gallas
    • 1
    • 2
    • 4
  • Jason A. C. Gallas
    • 1
    • 2
    • 4
  1. 1.Instituto de Altos Estudos da ParaíbaJoão PessoaBrazil
  2. 2.Departamento de FísicaUniversidade Federal da ParaíbaJoão PessoaBrazil
  3. 3.Faculdade de Ciências, Instituto Dom LuizUniversidade de LisboaLisbonPortugal
  4. 4.Complexity Sciences CenterSurfsideUSA

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