Critical behavior of the Lyapunov exponent in type-III intermittency

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

Chaos, Solitons & Fractals, 2008, vol. 36, issue 1, 150-156

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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:36:y:2008:i:1:p:150-156

DOI: 10.1016/j.chaos.2006.06.017

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