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Naimark–Sacker bifurcations in a delay quartic map

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  • Rech, Paulo C.

Abstract

In this paper, we consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark–Sacker bifurcation. We investigate, via numerical simulations, phenomena associated with the appearance, in the phase-space, of closed invariant curves involved in the Naimark–Sacker bifurcation. Lyapunov exponents, parameter-space and phase-space diagrams are used to show that the transition from quasiperiodic to chaotic states generally do not happen in this case. We determine numerically the location of the parameter sets where the Naimark–Sacker bifurcation occurs.

Suggested Citation

  • Rech, Paulo C., 2008. "Naimark–Sacker bifurcations in a delay quartic map," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 387-392.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:2:p:387-392
    DOI: 10.1016/j.chaos.2006.08.029
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    References listed on IDEAS

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    1. Peng, Mingshu, 2005. "Rich dynamics of discrete delay ecological models," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1279-1285.
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