Search

We consider a single Chua's circuit and a system of a unidirectionally coupled n-Chua's circuits driven by a biharmonic signal with two widely different frequencies ω and Ω, where Ω ≫ ω. We show experimental evidence for vibrational resonance in the single Chua's circuit and undamped signal propagation of a low-frequency signal in the system of n-coupled Chua's circuits where only the first circuit is driven by the biharmonic signal. In the single circuit, we illustrate the mechanism of vibrational resonance and the influence of the biharmonic signal parameters on the resonance. In the n(=75)-coupled Chua's circuits enhanced propagation of low-frequency signal is found to occur for a wide range of values of the amplitude of the high-frequency input signal and coupling parameter. The response amplitude of the ith circuit increases with i and attains a saturation. Moreover, the unidirectional coupling is found to act as a low-pass filter. [ABSTRACT FROM AUTHOR]

Detecting determinism in univariate and multivariate time series is difficult if the underlying process is nonlinear, and the noise level is high. In a previous paper, the authors proposed a method based on observable ordinal patterns. This method exploits the robustness of admissible ordinal patterns against observational noise, and the super-exponential growth of forbidden ordinal patterns with the length of the patterns. The new method compared favorably to the Brock-Dechert-Scheinkman independence test when applied to time series projected from the Hénon attractor and contaminated with Gaussian noise of different variances. In this paper, we extend this comparison to higher fractal dimensions by using noisy orbits on the attractors of the Lorenz map, and the time-delayed Hénon map. Finally, we make an analysis that enlightens the robustness of admissible ordinal patterns in the presence of observational noise. [ABSTRACT FROM AUTHOR]

We have proposed an adaptive procedure in order to estimate unknown parameters of a numerical model of a chaotic CO2 laser, which is observed through a time series that represents the output intensity of the laser. To do that, we consider a coupled system with the same functional form and adjustable parameters. The salient feature of the proposed technique is that accurate parameter estimation and identical synchronization can be jointly achieved by adaptively adjusting the desired parameters of the coupled system. [ABSTRACT FROM AUTHOR]

The brain can be described as a very complex dynamical system whose autonomous, intrinsic activity is modulated by a great variety of external inputs. In the last decade, the simulation of this activity by using networks of neurons has led to the development of new approaches to describe the processing of information by the nervous system. In this review paper we focus on winnerless competition, a new concept allowing the analysis of the emergent behavior associated with collective synchronization, multi-stability and adaptation — properties which seem to be at the basis of brain performance. The relationship between winnerless competition and the concept of chaotic itinerancy is stressed by pointing out their common association with the formation of complex heteroclinic orbits in the high-dimensional phase space associated with the dynamics of complex neuronal systems. The potentialities of networks of coupled map neurons to the study of activation and synchronization regimes in neural systems are suggested by means of different simulations showing a great variety of dynamical phenomena. [ABSTRACT FROM AUTHOR]