Experimental observation of coherence resonance in cascaded excitable systems

Postnov, Dmitry E.; Han, Seung Kee; Yim, Tae Gyu; Sosnovtseva, Olga

doi:10.1103/physreve.59.r3791

Cited by 119 publications

(69 citation statements)

References 11 publications

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“…This approach was successful in interpreting CR in neuron models [PK97; LNK98; LSG00]. CR in excitable systems was experimentally confirmed in a laser diode with optical feedback [GGBT00] and in electronic circuits [PHYS99]. CR has also been observed in bistable systems such as in simulations of the FitzHugh-Nagumo model [LSG00], and both in simulations and experiments with the chaotic Chua model [CMT01; PTMC01].…”

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confidence: 93%

Self-Organization in Semiconductor Lasers with Ultrashort Optical Feedback

et al. 2004

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In this work, self-organization in semiconductor lasers with ultra-short optical feedback is investigated. Exploiting dc currents to tune the relevant feedback parameters, we have experimentally prepared and studied a number of novel nonlinear dynamical scenarios.Two different types of self-sustaining intensity-pulsations are detected depending on strength and phase of the feedback. One type of pulsations is emerging in a Hopf-bifurcation from relaxation oscillations. These oscillations become undamped due to dispersive self-Q switching. The second type of pulsations is a beating of distinct compound-cavity modes. It is also born in a Hopf bifurcation. These findings represent experimental evidence for theoretical predictions. A supplementary mode and stability analysis agrees well with measurements.Coexistence of mode beating and relaxation oscillations gives rise to the break-up of regular pulsations into chaotic emission via a quasi-periodic route to chaos. The sudden destruction of chaos is indicative of a boundary crisis scenario, in which we see a discontinuous disappearance of an attractor. The existence of chaotic saddles underlying transient chaotic dynamics which appears behind boundary crisis is experimentally verified. It is experimentally demonstrated that an excitation of chaotic transients is closely related to a conventional excitability. The experiment is supplemented by numerical simulations.The influence of external Gaussian noise close to the onset of sub-and super-critical Hopf bifurcations is studied. Noise-induced oscillations appear as a noisy precursor with Lorentzian shape peak in the power spectrum. The coherence factor defined by the product of height and quality factor exhibits non-monotonic behavior with a distinct maximum at a certain noise intensity for both types of Hopf bifurcations, demonstrating coherence resonance. Besides these similarities, the measurements reveal also qualitative differences between the two cases. Whereas the width of the noise induced peak increases monotonically with noise intensity for the supercritical bifurcation, it traverses a pronounced minimum in the subcritical case. The experimental findings are examined in terms of general model for the noise driven motion close to bifurcations. Keywords

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confidence: 93%

Self-Organization in Semiconductor Lasers with Ultrashort Optical Feedback

et al. 2004

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We demonstrate the existence of noise-induced periodicity (coherence [16,17], spatio-temporal arrays [18,19] and a few experimental systems [13,15,[20][21][22][23][24].

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confidence: 99%

Coherence resonance in models of an excitable neuron with noise in both the fast and slow dynamics

Hilborn

Erwin

2004

Physics Letters A

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“…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].…”

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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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Experimental observation of coherence resonance in cascaded excitable systems

Cited by 119 publications

References 11 publications

Self-Organization in Semiconductor Lasers with Ultrashort Optical Feedback

Self-Organization in Semiconductor Lasers with Ultrashort Optical Feedback

Coherence resonance in models of an excitable neuron with noise in both the fast and slow dynamics

Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch

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