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Critical behavior of the Lyapunov exponent in type-III intermittency

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  • Alvarez-Llamoza, O.
  • Cosenza, M.G.
  • Ponce, G.A.

Abstract

The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent β expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that β varies on the interval 0⩽β<1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent β implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition.

Suggested Citation

  • Alvarez-Llamoza, O. & Cosenza, M.G. & Ponce, G.A., 2008. "Critical behavior of the Lyapunov exponent in type-III intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 150-156.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:1:p:150-156
    DOI: 10.1016/j.chaos.2006.06.017
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    1. Russo, Lucia & Altimari, Pietro & Mancusi, Erasmo & Maffettone, Pier Luca & Crescitelli, Silvestro, 2006. "Complex dynamics and spatio-temporal patterns in a network of three distributed chemical reactors with periodical feed switching," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 682-706.
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    Cited by:

    1. Zribi, Mohamed & Oteafy, Ahmed & Smaoui, Nejib, 2009. "Controlling chaos in the permanent magnet synchronous motor," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1266-1276.

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