Journal ArticleDOI
Theory of intermittency
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TLDR
In this article, aperiodic or chaotic behavior for one-dimensional maps just before a tangent bifurcation occurs appears as intermittency in which long laminar-like regions irregularly separated by bursts occur.Abstract:
The aperiodic or chaotic behavior for one-dimensional maps just before a tangent bifurcation occurs appears as intermittency in which long laminarlike regions irregularly separated by bursts occur. Proceeding from the picture proposed by Pomeau and Manneville, numerical experiments and analytic calculations are carried out on various models exhibiting this behavior. The behavior in the presence of external noise is analyzed, and the case of a general power dependence of the curve near the tangent bifurcation is studied. Scaling relations for the average length of the laminar regions and deviations from scaling are determined. In addition, the probability distribution of path lengths, the stationary distribution of the maps, the correlation function and power spectrum of the map in the intermittent region, and the Lyapunov exponent are obtained.read more
Citations
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Journal ArticleDOI
Fluctuations and simple chaotic dynamics
TL;DR: In this paper, the effects of fluctuations on the period-doubling bifurcation to chaos were investigated and the scaling behavior of the Lyapunov characteristic exponent near the transition to chaos was verified.
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Observations of order and chaos in nonlinear systems
TL;DR: In this paper, the authors illustrate the following transition sequences; period doubling and the U-sequence, intermittency, the periodic-quasiperiodic-chaotic sequence, frequency locking, and an alternating periodic-chotic sequence.
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Noisy precursors of nonlinear instabilities
TL;DR: In this article, the effect of external noise on systems displaying nonlinear instabilities of periodic orbits was studied, and each class of instability was found to have its own characteristic signature, as displayed by the power spectrum.
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Chaos in neurobiology
TL;DR: The authors show that chaotic dynamics are expected in nonlinear feedback systems possessing time delays such as are found in recurrent inhibition and from the periodic forcing of neural oscillators.
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Characterisation of intermittency in chaotic systems
TL;DR: In this article, the authors discuss the characterisation of intermittency in chaotic dynamical systems by means of the time fluctuations of the response to a slight perturbation on the trajectory.
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