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Combined effects of the damping and forcing in the underdamped time-delayed Duffing oscillator are considered in this paper. We analyse the generation of a certain damping-induced unpredictability due to the gradual suppression of interwell oscillations. We find the minimal amount of the forcing amplitude and the right forcing frequency to revert the effect of the dissipation, so that the interwell oscillations can be restored, for different time delay values. This is achieved by using the delay-induced resonance, in which the time delay replaces one of the two periodic forcings present in the vibrational resonance. A discussion in terms of the time delay of the critical values of the forcing for which the delay-induced resonance can tame the dissipation effect is finally carried out. [ABSTRACT FROM AUTHOR]

The predictability of a system indicates how much time a computed orbit is close to an actual orbit of the system, independent of its stability or chaotic nature. We derive a predictability index from the distributions of finite-time Lyapunov exponents of several prototypical orbits, both regular and irregular, in a variety of galactic potentials. In addition, by analysing the evolution of the shapes of the distributions with the finite-time intervals sizes, we get an insight into the time-scales of the model when the flow dynamics evolve from the local to the global regime. [ABSTRACT FROM AUTHOR]

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]

In this brief, we analyze a kind of chaos-coded modulations over both Rician and Rayleigh frequency non-selective un-correlated fading in the presence of additive white Gaussian noise. We provide bounds both for the case when perfect channel-state information (CSI) is available at the decoder and when there is no CSI. We show that the bounds proposed can be tight enough to give reason of the behavior of these systems in a flat fading channel. We compare the results with a related trellis-coded modulation and show that the degradation in performance can be at least as low as with conventional coded modulation systems. [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]

A known maximum a posteriori (MAP) algorithm is adapted to decode chaotic signals sent over a noisy channel and get a low complexity MAP decoder that could be easily implemented. It is shown that this algorithm is useful for all chaotic encoding frameworks where symbolic dynamics could be applied and that the final bit error rate is better than that obtained with other usually employed maximum likelihood (ML) algorithms of similar complexity. [ABSTRACT FROM AUTHOR]

We report our investigation on the effect of multiple time-delay on vibrational resonance in a single Duffing oscillator and in a system of n Duffing oscillators coupled unidirectionally and driven by both a low- and a high-frequency periodic force. For the single oscillator, we obtain analytical expressions for the response amplitude Q and the amplitude g of the high-frequency force at which resonance occurs. The regions in parameter space of enhanced Q at resonance, as compared to the case in absence of time-delay, show a bands-like structure. For the two-coupled oscillators, we explain all the features of variation of Q with the control parameter g. For the system of n-coupled oscillators with a single time-delay coupling, the response amplitudes of the oscillators are shown to be independent of the time-delay. In the case of a multi time-delayed coupling, undamped signal propagation takes place for coupling strength (δ) above a certain critical value (denoted as δu). Moreover, the response amplitude approaches a limiting value QL with the oscillator number i. We obtain analytical expressions for both δu and QL. [ABSTRACT FROM AUTHOR]

The influence of linear time-delayed feedback on vibrational resonance is investigated in underdamped and overdamped Duffing oscillators with double-well and single-well potentials driven by both low frequency and high frequency periodic forces. This task is performed through both theoretical approach and numerical simulation. Theoretically determined values of the amplitude of the high frequency force and the delay time at which resonance occurs are in very good agreement with the numerical simulation. A major consequence of time-delayed feedback is that it gives rise to a periodic or quasiperiodic pattern of vibrational resonance profile with respect to the time-delayed parameter. An appropriate time delay is shown to induce a resonance in an overdamped single-well system which is otherwise not possible. For a range of values of the time-delayed parameters, the response amplitude is found to be larger than in delay-time feedback-free systems. [ABSTRACT FROM AUTHOR]

We use the Hénon-Heiles system as a paradigmatic model for chaotic scattering to study the Lorentz factor effects on its transient chaotic dynamics. In particular, we focus on how time dilation occurs within the scattering region by measuring the time with a clock attached to the particle. We observe that the several events of time dilation that the particle undergoes exhibit sensitivity to the initial conditions. However, the structure of the singularities appearing in the escape time function remains invariant under coordinate transformations. This occurs because the singularities are closely related to the chaotic saddle. We then demonstrate using a Cantor-like set approach that the fractal dimension of the escape time function is relativistic invariant. In order to verify this result, we compute by means of the uncertainty dimension algorithm the fractal dimensions of the escape time functions as measured with an inertial frame and a frame comoving with the particle. We conclude that, from a mathematical point of view, chaotic transient phenomena are equally predictable in any reference frame and that transient chaos is coordinate invariant. [ABSTRACT FROM AUTHOR]