Chaos suppression through asymmetric coupling

Bragard, J.; Vidal, Gerard; Mancini, H.; Mendoza, Carolina; Boccaletti, Stefano

doi:10.1063/1.2797378

Cited by 29 publications

(15 citation statements)

References 28 publications

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“…Synchronization regime has been analyzed using different coupling schemes (symmetric or asymmetric) and considering the coupling as a direct function of the error between both systems (acting as a feedback loop). Phase synchronization (PS) has been obtained using selected values for parameters that must be fine-tuned to fit the Lyapunov exponent windows [21]. The synchronized regimes obtained in this case are not very stable and depend strongly on the coupling coefficient value.…”

Section: The Coupled Systemmentioning

confidence: 99%

Dynamics of two coupled chaotic systems driven by external signals

Mancini

Vidal

2010

Eur. Phys. J. D

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Abstract. Setting-up a controlled or synchronized state in a space-time chaotic structure targeting an unstable periodic orbit is a key feature of many problems in high dimensional physical, electronics, biological and ecological systems (among others (2000)]. In that case the flow was generated in a small container with inhomogeneous heating in order to have a single roll structure produced by a Bénard-Marangoni instability [E.L. Koshmieder, Bénard Cells and Taylor Vortices (Cambridge University Press, 1993)]. Phase synchronization was achieved by a small amplitude signal injected at a subharmonic frequency obtained from the measured Fourier temperature spectrum. In this work, we analyze numerically the effects of driving two previously synchronized chaotic oscillators by an external signal. The numerical system represents a convective experiment in a small container with square symmetry, where boundary layer instabilities are coupled by a common flow. This work is an attempt to control this situation and overcome some difficulties to select useful frequency values for the driving force, analyzing the influence of different harmonic injection signals on the synchronization in a system composed by two identical chaotic Takens-Bogdanov equations (TBA and TBB) bidirectionally coupled.

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Section: The Coupled Systemmentioning

confidence: 99%

Dynamics of two coupled chaotic systems driven by external signals

Mancini

Vidal

2010

Eur. Phys. J. D

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“…Bragard et al [20] observed chaos suppression in chaotic oscillators with bidirectional asymmetric coupling. They found that adequate asymmetry and coupling between two identical chaotic oscillators may force their dynamics towards regular periodic oscillations.…”

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confidence: 99%

Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch

Pisarchik

Jaimes-Reátegui

2015

Phys. Rev. E

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A small mismatch between natural frequencies of unidirectionally coupled chaotic oscillators can induce coherence resonance in the slave oscillator for a certain coupling strength. This surprising phenomenon resembles "stabilization of chaos by chaos," i.e., the chaotic driving applied to the chaotic system makes its dynamics more regular when the natural frequency of the slave oscillator is a little different than the natural frequency of the master oscillator. The coherence is characterized with the dominant component in the power spectrum of the slave oscillator, normalized standard deviations of both the peak amplitude and the interpeak interval, and Lyapunov exponents. The enhanced coherence is associated with increasing negative both the third and the fourth Lyapunov exponents, while the first and second exponents are always positive and zero, respectively. It is common knowledge that a nonlinear system in the presence of noise can exhibit resonance phenomena such as stochastic [1,2] or coherence [3] resonance. While the former is seen as an optimal response to external periodic modulation with respect to the noise intensity, the latter manifests itself as increasing regularity in one of the system internal time scales without additional modulation. Coherence resonance was detected first in excitable dynamical systems [3][4][5][6][7] and then in bistable systems [8][9][10]. Examples are typically found in biology in the form of neuron spiking dynamics [11].Analogous phenomena were observed in deterministic chaotic systems without noise, since an external chaotic forcing acts in a similar way as noise. Deterministic stochastic resonance was found in bistable chaotic systems [12][13][14] and deterministic coherence resonance in chaotic systems with delayed feedback [15][16][17] including diffusively coupled Rössler oscillators [18]. In laser applications, an increase in the injection diode current leads to an optimal regularity of chaotic laser diode power dropouts [15,16].It is not surprising that synchronization can affect chaotic dynamics [19]. Bragard et al. [20] observed chaos suppression in chaotic oscillators with bidirectional asymmetric coupling. They found that adequate asymmetry and coupling between two identical chaotic oscillators may force their dynamics towards regular periodic oscillations. Since this phenomenon occurs for the value of the coupling strength well below the value for complete synchronization, it was interpreted as a generalized synchronization state.In this Rapid Communication, we report on a significantly different case of deterministic coherence resonance. We consider two unidirectionally coupled nonidentical chaotic oscillators, masterẋ 1 = F(x 1 ,ω 1 ) and slaveẋ 2 = F(x 2 ,ω 2 ) + σ (x 1 − x 2 ), where x 1,2 are state variables of the master and slave systems, F is a vector function, and σ is a coupling strength. The oscillators are only distinguished by their natural * apisarch@cio.mx frequencies ω 1 and ω 2 . Due to nonlinearity, the dominant frequency ω 0 in the chaoti...

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“…Phase synchronization (PS) has been obtained using selected values for parameters that must be fine-tuned to fit Lyapunov exponent windows. 25 The synchronized regimes obtained in this case are not too stable and depend strongly on the coupling coefficient.…”

Section: Coupling Effectsmentioning

confidence: 77%

“…Synchronization induced by asymmetric coupling (masterslave configuration) of two or more autonomous oscillators is a well-known effect. 25,28 In four dimensional systems (4D) with symmetrical coupling of two identical T-B systems, one variable (x) has been presented in Ref. 28.…”

Section: Coupling Effectsmentioning

confidence: 99%

“…22 In particular, chaos suppression by coupling two systems was demonstrated in 3D systems coupling asymmetrically two classical chaotic oscillators. 25 In this work, two identical Rössler (in funnel and no-funnel regimes), two Lorenz, and two Lotka-Volterra systems of equations have been coupled. The method used here with three 3D systems rests on selecting an adequate coupling in order to drive a chaotic dynamics towards a regular periodic attractor.…”

Section: Introductionmentioning

confidence: 99%

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Control and synchronization of hyperchaotic states in mathematical models of Bènard-Marangoni convective experiments

Mancini

Becheikh²,

Vidal³

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Mathematical models are of great interest for experimentalists since they provide a way for controlling and synchronizing different chaotic states. In previous works, we have used a Takens-Bogdanov (T-B) system under hyperchaotic dynamic conditions (two or more positive Lyapunov exponents) because they adequately reflect the dynamics of the patterns in small aspect ratio pre-turbulent Bènard-Marangoni convection near a codimension-2 point (with resonance between 2:1 modes), in square symmetry (D4). In this paper, we discuss the coupling of two different four dimensional hyperchaotic models derived from the Lorenz equations by using the same method introduced in previous works. As in the former system of used equations, we found that two identical hyperchaotic systems based on either Chen or Lü equation systems evolve into different states in the pattern space, where the synchronization state or the complexity could be controlled by a small external signal, as was shown in T-B equations.

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Chaos suppression through asymmetric coupling

Cited by 29 publications

References 28 publications

Dynamics of two coupled chaotic systems driven by external signals

Dynamics of two coupled chaotic systems driven by external signals

Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch

Control and synchronization of hyperchaotic states in mathematical models of Bènard-Marangoni convective experiments

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