Incomplete noise-induced synchronization of spatially extended systems

Hramov, Alexander E.; Короновский, А. А.; Popov, P. V.

doi:10.1103/physreve.77.036215

Cited by 21 publications

(11 citation statements)

References 25 publications

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“…At the same time, not only is the largest Lyapunov exponent value important to characterize the system dynamics. For example, the zero Lyapunov exponent plays a significant role for different phenomena, such as for the quasiperiodic oscillations or for the different types of the synchronous motion such as the phase synchronization [24][25][26][27] or incomplete noise-induced synchronization [28].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov exponent corresponding to enslaved phase dynamics: Estimation from time series

2015

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A method for the estimation of the Lyapunov exponent corresponding to enslaved phase dynamics from time series has been proposed. It is valid for both nonautonomous systems demonstrating periodic dynamics in the presence of noise and coupled chaotic oscillators and allows us to estimate precisely enough the value of this Lyapunov exponent in the supercritical region of the control parameters. The main results are illustrated with the help of the examples of the noised circle map, the nonautonomous Van der Pole oscillator in the presence of noise, and coupled chaotic Rössler systems.

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Section: Introductionmentioning

confidence: 99%

Lyapunov exponent corresponding to enslaved phase dynamics: Estimation from time series

2015

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“…The above factors require a development of specific approaches to stability analysis of various spatially extended systems. 16,[19][20][21][22] In this paper, we propose an approach for the calculation of the spectrum of Lyapunov exponents for a system of coupled Poisson and continuity equations, and apply this method to a strongly coupled semiconductor superlattice (SL) operating in the miniband transport regime. 23,24 We should note that for weakly coupled SLs, in which the resonant tunneling transport mechanism dominates, the charge dynamics can be described by a spatially discrete version of the Poisson and continuity equations.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov stability of charge transport in miniband semiconductor superlattices

et al. 2013

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“…The stochastic or noise induced synchronization can be observed in spatially distributed dynamic sys tems containing additive spatially temporal noise. It appears due to the interaction of the determined and stochastic dynamics and is the subject of numerous investigations of physical, chemical, biological, and other systems, which describe nonlinear effects, in recent time [11][12][13][14].…”

Section: Noise Induced Synchronization In a Spatially Distributed Sysmentioning

confidence: 99%

Noise-induced synchronization in a spatially distributed system with a 1/f spectrum

Koverda

Skokov

2015

Dokl. Phys.

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193Stable physical systems and processes are charac terized by the Lorentzian spectrum of fluctuation power, at which low frequency pulsations are inde pendent of frequency, while high frequency ones descend inversely proportional to the frequency quad rate. Fluctuations are small as a rule and follow the Gaussian distribution. The relaxation of perturbation in such processes occurs following the descend expo nent. The entropy of the stable state is maximal. Large fluctuations spontaneously appear in complex statistic systems that are far from equilibrium. A considerable part of the energy of such pulsations is associated with slow processes and is accumulated at low frequencies; therefore, large scale high energy emissions are possi ble [1]. Such fluctuations have a power spectrum inversely proportional to the frequency: .Another characteristic feature of such fluctuations is the scale invariant distribution function, which has power "tails." In this case, the perturbation relaxation descends not exponentially but following the power law. Such a situation occurs in the thermodynamic critical point of the liquid-vapor phase transition. The scale invariance of fluctuations of thermodynamic quantities near the critical point [2] is determined by the approaching conditions of properties of various phases and requires the exact tuning and large relax ation times. In contrast with the thermodynamic crit ical point, nonequilibrium processes with large fluctu ations point to their stable spatial and temporal scale invariance without fine tuning the parameters. There fore, the appearance of 1/f fluctuations is often associ 1 ( )S f f ated with the concept of self organized criticality [3], which describes the avalanche dynamics and is applied to demonstrate the criticality of the behavior in numerous computer models. Fractional integration of white noise is applied for the mathematical description of random processes with the 1/f spectrum of fluctuations [4], but it is diffi cult to associate it with the physical properties of the system. Fluctuations in a broad range of scales are also developed in turbulent flows of liquid [5]. The appear ance of extreme fluctuations is possible under the effect of white noise in interacting phase transitions. Extreme fluctuations manifest themselves in thermalphysical systems with phase transitions as pulsations of flows in critical and transient modes of heat and mass transfer [6]. When describing the processes with extreme fluctuations, a set of nonlinear stochastic equations that describe the interacting nonequilib rium phase transitions is used [7]:(1)where and are dynamic variables, and is the Gaussian white noise, = , and is the amplitude of the white noise. The criticality of set (1) corresponds to a level of white noise that corresponds to the transition induced by the noise [7]. A random process, which is described by set (1), has a 1/f spectrum of fluctuation power. This is accompanied by the accumulation of fluctuation energy at low frequencies, and the process is character...

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Incomplete noise-induced synchronization of spatially extended systems

Cited by 21 publications

References 25 publications

Lyapunov exponent corresponding to enslaved phase dynamics: Estimation from time series

Lyapunov exponent corresponding to enslaved phase dynamics: Estimation from time series

Lyapunov stability of charge transport in miniband semiconductor superlattices

Noise-induced synchronization in a spatially distributed system with a 1/f spectrum

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