Intermittent transient chaos at interior crises in the diode resonator

Rollins, R. W.; Hunt, E. Raymond

doi:10.1103/physreva.29.3327

Cited by 63 publications

(22 citation statements)

References 18 publications

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“…For interior crises which terminate a periodic window the dependence of MLE on the control parameter is sigmoidal, with a large increase in fluctuations subsequent to the crisis. This abrupt increase in the MLE at interior crises has been observed before [6,7,8,9,10] in some studies of 1 − d and 2 − d maps and flows. In contradistinction the MLE only has a "knee" at attractor-merging crises: after the crisis, the rate of change of the Lyapunov exponent decreases significantly.…”

Section: Introductionmentioning

confidence: 97%

Maximal Lyapunov exponent at crises

Mehra

Ramaswamy

1996

Phys. Rev. E

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We study the variation of Lyapunov exponents of simple dynamical systems near attractor-widening and attractor-merging crises. The largest Lyapunov exponent has universal behaviour, showing abrupt variation as a function of the control parameter as the system passes through the crisis point, either in the value itself, in the case of the attractor-widening crisis, or in the slope, for attractor merging crises. The distribution of local Lyapunov exponents is very different for the two cases: the fluctuations remain constant through a merging crisis, but there is a dramatic increase in the fluctuations at a widening crisis.

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Section: Introductionmentioning

confidence: 97%

Maximal Lyapunov exponent at crises

Mehra

Ramaswamy

1996

Phys. Rev. E

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“…Just above V c regions of the system still spend long periods of time trapped in the old two-band attractor before switching to the new single attractor for a time and then back again. In a single chaotic oscillator the intermittent switching between two attractors is an example of crisis-induced intermittency and the trap time displays exponentially distributed switching times [19]. As discussed below, crisis-induced intermittency also exists in coupled system but the trap time at that point is now dominated by stretched exponentials.…”

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confidence: 99%

“…Just above the crisis the system gets trapped in the two-band attractor in local regions for a while before going chaotic again. While for an uncoupled system the times between switches have a long-time exponential distribution [19], Fig. 6 shows that the traptime distribution for this model follows a stretched exponential with β = 0.70 ± 0.05 over the full distribution, with all sites displaying the same distribution.…”

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confidence: 99%

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Stretched-exponential dynamics in a chain of coupled chaotic oscillators

2002

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Abstract. -We measure stretched exponential behavior, exp −(t/τ0) β , over many decades in a one-dimensional array of coupled chaotic electronic elements just above a crisis-induced intermittency transition. There is strong spatial heterogeneity and individual sites display a dynamics ranging from near power law (β = 0) to near exponential (β = 1) while the global dynamics, given by a spatial average, remains stretched exponential. These results can be reproduced quantitatively with a one-dimensional coupled-map lattice and thus appear to be system independent. In this model, local stretched exponential dynamics is achieved without frozen disorder and is a fundamental property of the coupled system. The heterogeneity of the experimental system can be reproduced by introducing quenched disorder in the model. This suggests that the stretched exponential dynamics can arise as a purely chaotic phenomenon.Stretched exponential relaxation is almost ubiquitous in complex systems. It is found in glasses [1], spin glasses [2], polymers, high-dimensional cellular automata [3], random networks [4] coupled chaotic oscillators [5,6] and others [7]. For many of these problems, however, the microscopic origin of this dynamics is difficult to establish both experimentally and theoretically. Understanding the underlying causes for stretched exponential relaxation remains, therefore, a central goal in the study of the dynamics of complex systems [8][9][10], as witnessed by the flurry of theoretical, experimental and numerical results that have appeared on the subject in the last few years [10][11][12][13].In the last 20 years, many physical processes have been understood in terms of nonlinear dynamics and chaos, these concepts often going beyond the reach of standard equilibrium statistical physics. Here, we present experimental results showing a stretched exponential dynamics, exp −(t/τ 0 ) β , in a simple one-dimensional chaotic system comprised of a chain of chaotic electronic oscillators. In particular, we find that in the vicinity of the transition to spatiotemporal chaos, individual site dynamics shows this behavior over six orders of magnitude and that the β's associated with individual site range from 0.8 (nearly exponential) to 0.2

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“…(10) We shall now calculate the maximal height of the peak at tmjfl. It should be attained for values of a for which the left boundaries of I,, and 'esc,L coincide.…”

Section: +1/-mentioning

confidence: 99%