Statistical dynamics of sine-square map

P. Philominathan, P. Neelamegam and S. Rajasekar

Physica A: Statistical Mechanics and its Applications, 1997, vol. 242, issue 3, 391-408

Abstract: In this paper we study (i) the variation of local Lyapunov exponent, (ii) characterization of chaotic attractor at bifurcations using the variance σn(q) of fluctuations of coarse-grained local expansion rates of nearby orbits and (iii) characterization of weak and strong chaos in a sine-square map which describes the dynamics of the liquid crystal hybrid optical bistable device. The standard deviation of local Lyapunov exponent λ(X,L) calculated after every L time steps and Allan variance are found to approach zero in the limit L → ∞ as L−α. For all chaotic attractors of the map the σn(q) versus q plot exhibits a peak at q = qα. We show that additional peaks, however, occur only for the attractors just before and just after the bifurcations. We investigate the characteristics of the probability distributions of a k-step difference quantity ΔXk=Xi+k−Xi. We show that a nonstationary probability distribution occurs for weak chaos and a stationary distribution occurs for strong chaos.

Keywords: Sine-square map; Local Lyapunov exponent; Dynamical structure functions; Strong and weak chaos (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:242:y:1997:i:3:p:391-408

DOI: 10.1016/S0378-4371(97)00259-8

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