Collective response in globally coupled bistable systems

Jung, P.; Behn, Ulrich; Pantazelou, Eleni; Moss, Frank

doi:10.1103/physreva.46.r1709

Cited by 182 publications

(112 citation statements)

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“…The above consideration shows that changing the number of elements in a small ensemble of coupled bistable elements to the optimum can significantly improve the sensitivity (cf. [5]). Moreover, changing its connectivity and/or coupling strength, a neuronal system can tune itself to signals with different frequencies.…”

Section: P H Y S I C a L R E V I E W L E T T E R S 4 February 2002mentioning

confidence: 99%

“…Stochastic resonance has been observed in numerous experiments [3]. Noteworthy, the order in a noise-driven system can have a maximum at a certain noise level even in the absence of periodic forcing, this phenomenon being called coherence resonance [4].Being first discussed in the context of a simple bistable model, stochastic resonance has been also studied in complex systems consisting of many elementary bistable cells [5]; moreover, the resonance may be enhanced due to coupling [6]. In this paper we discuss another type of resonance in such systems, namely, the system size resonance, when the dynamics is maximally ordered at a certain number of interacting subsystems.…”

mentioning

confidence: 99%

“…Being first discussed in the context of a simple bistable model, stochastic resonance has been also studied in complex systems consisting of many elementary bistable cells [5]; moreover, the resonance may be enhanced due to coupling [6]. In this paper we discuss another type of resonance in such systems, namely, the system size resonance, when the dynamics is maximally ordered at a certain number of interacting subsystems.…”

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confidence: 99%

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System Size Resonance in Coupled Noisy Systems and in the Ising Model

2002

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We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensembles -lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance. DOI: 10.1103/PhysRevLett.88.050601 PACS numbers: 05.40.Ca, 05.45. -a, 05.50. +q Stochastic resonance has attracted much interest recently [1]. As was demonstrated in [2], a response of a noisy nonlinear system to a periodic forcing can exhibit a resonancelike dependence on the noise intensity. In other words, there exists a "resonant" noise intensity at which the response to a periodic force is maximally ordered. Stochastic resonance has been observed in numerous experiments [3]. Noteworthy, the order in a noise-driven system can have a maximum at a certain noise level even in the absence of periodic forcing, this phenomenon being called coherence resonance [4].Being first discussed in the context of a simple bistable model, stochastic resonance has been also studied in complex systems consisting of many elementary bistable cells [5]; moreover, the resonance may be enhanced due to coupling [6]. In this paper we discuss another type of resonance in such systems, namely, the system size resonance, when the dynamics is maximally ordered at a certain number of interacting subsystems. Contrary to previous reports of array-enhanced stochastic resonance (cf. also [7]), here we fix the noise strength, coupling, and other parameters; only the size of the ensemble changes.The basic model to be considered below is the ensemble of noise-driven bistable overdamped oscillators, governed by the Langevin equations,Here j i ͑t͒ is a Gaussian white noise with zero mean: ͗j i ͑t͒j j ͑t 0 ͒͘ d ij d͑t 2 t 0 ͒;´is the coupling constant; N is the number of elements in the ensemble, and f͑t͒ is a periodic force to be specified later. In the absence of periodic force, the model (1) has been extensively studied in the thermodynamic limit N !`. It demonstrates an Isingtype phase transition at´´c from the disordered state with vanishing mean field X N 21 P i x i to the "ferromagnetic" state with a nonzero mean field X 6X 0 [8].While in the thermodynamic limit the full description of the dynamics is possible, for finite system sizes we have mainly a qualitative picture: In the ordered phase the mean field X switches between the values 6X 0 and its average vanishes for all couplings. The rate of switchings depends on the system size and tends to zero as N !`.For us, the main importance is the fact that qualitatively the behavior of the mean...

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Section: P H Y S I C a L R E V I E W L E T T E R S 4 February 2002mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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System Size Resonance in Coupled Noisy Systems and in the Ising Model

2002

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“…Noise induced entrainment among coupled oscillators is found experimentally in Belousov-Zhabotinsky reactions and brain waves [7,8]. Stochastic resonance has been studied also in globally or locally coupled systems of many bistable elements and it was shown that the coupling can lead to the enhancement of the response [9,10,11,12]. Various types of Fokker-Planck equations have been used to study the stochastic resonance theoretically.…”

Section: Introductionmentioning

confidence: 99%

Stochastic synchronization in globally coupled phase oscillators

Sakaguchi

2002

Phys. Rev. E

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Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order parameter oscillation is enhanced in an intermediate range of noise strength for a globally coupled bistable system, and the order parameter oscillation is entrained to the external periodic force in an intermediate range of noise strength. These enhancement phenomena of the response of the order parameter in the deterministic equations are interpreted as stochastic resonance and stochastic synchronization in globally coupled systems.

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“…Basically, the stochastic resonance has four elements: nonlinear system, information-carrying input signal, noise, and performance measure [2]. Many kinds of nonlinear systems have demonstrated the stochastic resonance phenomena, such as static systems [3], dynamic systems [4] [19], discrete systems [21], and coupled systems [4] [20]. The traditional stochastic resonance requires the information-carrying signal to be weak and periodic.…”

Section: Introductionmentioning

confidence: 99%

Enhancement of Stochastic Resonance Using Optimization Theory

Jiang

Repperger

et al. 2006

Communications in Information and Systems

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Abstract. The traditional stochastic resonance is realized by adding an optimal amount of noise, while the parameter-tuning stochastic resonance is realized by optimally tuning the system parameters. This paper reveals the possibility to further enhance the stochastic resonance effect by tuning system parameters and adding noise at the same time using optimization theory. The further improvement of the maximal normalized power norm of the bistable double-well dynamic system with white Gaussian noise input can be converted to an optimization problem with constraints on system parameters and noise intensity, which is proven to have one and only one local maximum for the Gaussian-distributed weak input signal. This result is then extended to the arbitrary weak input signal case. For the purpose of practical implementation, a fast-converging optimization algorithm to search the optimal system parameters and noise intensity is also proposed. Finally, computer simulations are performed to verify its validity and demonstrate its potential applications in signal processing.

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Collective response in globally coupled bistable systems

Cited by 182 publications

References 21 publications

System Size Resonance in Coupled Noisy Systems and in the Ising Model

System Size Resonance in Coupled Noisy Systems and in the Ising Model

Stochastic synchronization in globally coupled phase oscillators

Enhancement of Stochastic Resonance Using Optimization Theory

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