On-off intermittency in a quasiperiodic driven nonlinear oscillator

Hun, Yu Young; Kim, Doo Chul; Kwak, Kuemchol; Lim, Tong Kun; Jung, Won-Ki

doi:10.1016/s0375-9601(98)00568-4

Cited by 4 publications

(1 citation statement)

References 15 publications

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“…The proposed condition is based on the observation of the mechanism of the bursting behavior. It is revealed that the bursting is due to the loss of the local transverse stability of the synchronization manifold [Huna et al, 1998]. Especially, the bursting behavior takes place in local time with positive local Lyapunov exponent, even when the largest CLE is negative [Muruganandam et al, 1999].…”

Section: Introductionmentioning

confidence: 99%

Supreme Local Lyapunov Exponents and Chaotic Impulsive Synchronization

Chen

Liu

2013

Int. J. Bifurcation Chaos

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Impulsively synchronized chaos with criterion from conditional Lyapunov exponent is often interrupted by desynchronized bursts. This is because the Lyapunov exponent cannot characterize local instability of synchronized attractor. To predict the possibility of the local instability, we introduce a concept of supreme local Lyapunov exponent (SLLE), which is defined as supremum of local Lyapunov exponents over the attractor. The SLLE is independent of the system trajectories and therefore, can characterize the extreme expansion behavior in all local regions with prescribed finite-time interval. It is shown that the impulsively synchronized chaos can be kept forever if the largest SLLE of error dynamical systems is negative and then the burst behavior will not appear. In addition, the impulsive synchronization with negative SLLE allows large synchronizable impulsive interval, which is significant for applications.2

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Section: Introductionmentioning

confidence: 99%

Supreme Local Lyapunov Exponents and Chaotic Impulsive Synchronization

Chen

Liu

2013

Int. J. Bifurcation Chaos

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Stochastic resonance in spatiotemporal on–off intermittency

Stȩpień¹,

Krawiecki²,

Kosiński³

2004

Chaos, Solitons & Fractals

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On-Off Intermittency in Stochastically Driven Electrohydrodynamic Convection in Nematics

1999

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We report on-off intermittency in electroconvection of nematic liquid crystals driven by a dichotomous stochastic electric voltage. With increasing voltage amplitude we observe laminar phases of undistorted director state interrupted by shorter bursts of spatially regular stripes. Near a critical value of the amplitude the distribution of the duration of laminar phases is governed over several decades by a power law with exponent −3/2. The experimental findings agree with simulations of the linearized electrohydrodynamic equations near the sample stability threshold.PACS numbers: 05.40.+j, 47.20.-k, 47.54.+r, 61.30-v Systems at a threshold of stability driven by a stochastic or chaotic process coupling multiplicatively to the system variables may exhibit on-off intermittency characterized by specific statistical properties of the intermittent signal. Quiescent (or laminar) periods (off-states) are interrupted by bursts of large variation (on-states); the duration of laminar periods is governed by power laws with exponents universal over a broad class of different systems. Early theoretical studies considered systems with few degrees of freedom modeled by differential equations [1] and mappings [2]. There is increasing interest in systems with many degrees of freedom [3], described by random map lattices [4], larger systems of coupled nonlinear elements [5], and partial differential equations [5,6]. Experimental results are available mainly for nonlinear electric circuits [7]; on-off intermittency was also observed in a spin wave experiment [8], in optical feedback [9], and a gas discharge plasma system [10]. Here we first report about on-off intermittency in a spatially extended dissipative system, viz. electroconvection (EC) in nematic liquid crystals driven by a stochastic voltage.EC in planarly aligned nematics is a standard system for pattern formation, for recent reviews see, e.g. [11]. In the presence of an electric field E a spontaneous fluctuation of the director leads due to the anisotropic conductivity to a formation of space charges which tend to destabilize the homogeneously ordered state. With increasing strength of the driving field one observes a hierarchy of convection patterns of increasing complexity. The patterns depend on external parameters such as amplitude, frequency and wave form of the driving voltage which are conveniently adjustable in the experiment. The hydrodynamic flow induces a modulation of the director field and thus of the effective indices of refraction which leads to transmission patterns easily observed with a microscope.In previous experiments, the superposition of a deterministic AC field with a stochastic field, E = E det (t) + E stoch (t), was studied. A variety of noise induced phenomena including stabilization or destabilization of the homogeneous state, and a change from continuous to discontinuous behaviour of the threshold as a function of the noise strength was observed [12][13][14][15][16] and has stimulated theoretical work [17,18].As long as the characteristi...

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On-off intermittency in a quasiperiodic driven nonlinear oscillator

Cited by 4 publications

References 15 publications

Supreme Local Lyapunov Exponents and Chaotic Impulsive Synchronization

Supreme Local Lyapunov Exponents and Chaotic Impulsive Synchronization

Stochastic resonance in spatiotemporal on–off intermittency

On-Off Intermittency in Stochastically Driven Electrohydrodynamic Convection in Nematics

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