Scaling of the Lyapunov exponent in type-III intermittent chaos

TL;DR

This paper investigates how the Lyapunov exponent scales near chaos transition in type-III intermittency, revealing a variable critical exponent that challenges previous predictions.

Contribution

It introduces a generic map analysis to determine the scaling behavior of the Lyapunov exponent and calculates a variable critical exponent $eta$.

Findings

Critical exponent $eta$ varies between 0 and 1.

Scaling behavior differs from earlier predictions.

Provides a generic framework for understanding type-III intermittency.

Abstract

The scaling behaviour of the Lyapunov exponent near the transition to chaos via type-III intermittency is determined for a generic map. A critical exponent $\beta$ expressing the scaling of the Lyapunov exponent as a function of both, the reinjection probability and the nonlinearity of the map is calculated. It is found that the critical exponent varies on the interval $0 < \beta < 1$. This contrasts with earlier predictions for the scaling behaviour of the Lyapunov exponent in type-III intermittency.