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Arnold tongues and quasiperiodicity in a prey–predator model

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  • Rosa, Cleiton
  • Correia, Marcos J.
  • Rech, Paulo C.

Abstract

We consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark–Sacker bifurcation. We investigate, via analytical and numerical simulations, phenomena associated with the appearance, in the parameter-space, of structures like Arnold tongues involved in the Naimark–Sacker bifurcation. We determine analytically the location of the parameter sets where Naimark–Sacker bifurcation occurs, and the location on this line where tongues of arbitrary period are born. Lyapunov exponents, bifurcation diagrams, parameter-space and phase-space diagrams are used to show the transition from quasiperiodic to chaotic states.

Suggested Citation

  • Rosa, Cleiton & Correia, Marcos J. & Rech, Paulo C., 2009. "Arnold tongues and quasiperiodicity in a prey–predator model," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2041-2046.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:2041-2046
    DOI: 10.1016/j.chaos.2007.09.094
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    References listed on IDEAS

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    1. Che, Yan-Qiu & Wang, Jiang & Si, Wen-Jie & Fei, Xiang-Yang, 2009. "Phase-locking and chaos in a silent Hodgkin–Huxley neuron exposed to sinusoidal electric field," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 454-462.
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