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

  • Joana G. Freire
  • Marcia R. Gallas
  • Jason A. C. GallasEmail author
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
    Email author
  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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