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Intermittency cascade

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  • San Martín, Jesús

Abstract

The presence of saddle-node bifurcation cascade in the logistic equation is associated with an intermittency cascade in a similar way as a saddle-node bifurcation is associated with an intermittency. We merge the concepts of bifurcation cascade and intermittency; the result is intermittency cascade in which multichannel intermittencies duplicate successively their number of channels. The birth of successive saddle-node channels is ruled by an equation identical to Feigenbaum’s one. Another new concept will emerge: an attractor of attractors, where all the intermittency cascades converge, as well as all Myrberg–Feigenbaum points whose structure will be described. Some of these phenomena have been already pointed out in the physical literature, however they have only been qualitatively described because the underlying dynamics was not understood. The quantitative approach underlies in the intrinsic properties of dynamical systems exposed by this new framework.

Suggested Citation

  • San Martín, Jesús, 2007. "Intermittency cascade," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 816-831.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:816-831
    DOI: 10.1016/j.chaos.2005.11.025
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