Stochastic Resonance in Coupled Oscillator Systems with Time Delay

Abstract

We investigate stochastic resonance in a globally coupled oscillator system with time delay. The system shows multistability of a desynchronized state and two synchronized states with different collective frequencies, which may be interpreted as multistable perception of ambiguous or reversible figures. Under the influence of a weak periodic external signal, the system exhibits a maximum in the signal-to-noise ratio at an optimum noise level -the characteristic signature of stochastic resonance. We also show stochastic resonance between two limit-cycles in the system. [S0031-9007 (99)08392-1] PACS numbers: 05.40. -a, 07.05.Mh, 42.66.Si, 87.10. + e Synchronization of oscillators has been the topic of much recent investigation [1-3]. Recent experiments [4]showed the synchronized oscillations of neuronal activity in the visual cortex of the cat suggesting that information processing is a cooperative process of neurons. A coupled oscillator model was suggested to understand the temporal and spatial coherence of the oscillations of neuronal activity [2]. The inclusion of time delay into the system is natural in the realistic consideration of finite transmission of interaction. Recently, it was shown that the coupled oscillator system with time delay exhibits multistability of synchronized and desynchronized states [5]. In the synchronized state, the system has also two limit-cycles with different collective frequencies; one is larger than the intrinsic frequency and the other is smaller than the intrinsic frequency. This multistability was interpreted as the perception of ambiguous or reversible figures. Perception of the ambiguous or reversible figures is characterized by noisy multistable dynamics, that is, the different interpretations of the figures are switched with a stochastic time course [6]. Recently, there have been studies on the noisy multistable dynamics in connection with the development of dynamical models of brain function during such switchings in perception [7].There has also been a growing interest in stochastic resonance (SR) associated with noisy nonlinear dynamical systems [8]. SR is characterized by the optimization of the response of the system to an input signal as a function of the input noise strength. The response of the system is measured by a signal-to-noise ratio (SNR) which shows a peak as a function of the input noise strength. This implies that noise may enhance the transmission of information. SR has been demonstrated in numerous physical experiments such as electronic trigger circuits [9], twomode ring lasers [10], and mammalian neuronal networks [11]. The possible importance of SR for the processing of information in neural systems seems evident at all levels of information processing. Indeed, it has long been recognized that noise can improve the performance of certain neural networks [12], and that an optimum noise level can achieve the maximum improvement. SR in low dimensional dynamical systems with attractors is by now a familiar phenomenon, but SR in spatially distributed sys...

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