Chaotic communication based on the particle-in-a-box electronic circuit

A secure communication system based on the error-feedback synchronization of the electronic model of the particle-in-a-box system is proposed. This circuit allows a robust and simple electronic emulation of the mechanical behavior of the collisions of a particle inside a box, exhibiting rich chaotic behavior. The required nonlinearity to emulate the box walls is implemented in a simple way when compared with other analog electronic chaotic circuits. A master/slave synchronization of two circuits exhibiting a rich chaotic behavior demonstrates the potentiality of this system to secure communication. In this system, binary data stream information modulates the bifurcation parameter of the particle-in-a-box electronic circuit in the transmitter. In the receiver circuit, this parameter is estimated using Pecora-Carroll synchronization and error-feedback synchronization. The performance of the demodulation process is verified through the eye pattern technique applied on the recovered bit stream. During the demodulation process, the error-feedback synchronization presented better performance compared with the Pecora-Carroll synchronization. The application of the particle-in-a-box electronic circuit in a secure communication system is demonstrated.

Assessing the performance of dynamical trajectory estimates

Estimating trajectories and parameters of dynamical systems from observations is a problem frequently encountered in various branches of science; geophysicists for example refer to this problem as data assimilation. Unlike as in estimation problems with exchangeable observations, in data assimilation the observations cannot easily be divided into separate sets for estimation and validation; this creates serious problems, since simply using the same observations for estimation and validation might result in overly optimistic performance assessments. To circumvent this problem, a result is presented which allows us to estimate this optimism, thus allowing for a more realistic performance assessment in data assimilation. The presented approach becomes particularly simple for data assimilation methods employing a linear error feedback (such as synchronization schemes, nudging, incremental 3DVAR and 4DVar, and various Kalman filter approaches). Numerical examples considering a high gain observer confirm the theory.

Movement Sonification: Effects on Motor Learning beyond Rhythmic Adjustments

Motor learning is based on motor perception and emergent perceptual-motor representations. A lot of behavioral research is related to single perceptual modalities but during last two decades the contribution of multimodal perception on motor behavior was discovered more and more. A growing number of studies indicates an enhanced impact of multimodal stimuli on motor perception, motor control and motor learning in terms of better precision and higher reliability of the related actions. Behavioral research is supported by neurophysiological data, revealing that multisensory integration supports motor control and learning. But the overwhelming part of both research lines is dedicated to basic research. Besides research in the domains of music, dance and motor rehabilitation, there is almost no evidence for enhanced effectiveness of multisensory information on learning of gross motor skills. To reduce this gap, movement sonification is used here in applied research on motor learning in sports. Based on the current knowledge on the multimodal organization of the perceptual system, we generate additional real-time movement information being suitable for integration with perceptual feedback streams of visual and proprioceptive modality. With ongoing training, synchronously processed auditory information should be initially integrated into the emerging internal models, enhancing the efficacy of motor learning. This is achieved by a direct mapping of kinematic and dynamic motion parameters to electronic sounds, resulting in continuous auditory and convergent audiovisual or audio-proprioceptive stimulus arrays. In sharp contrast to other approaches using acoustic information as error-feedback in motor learning settings, we try to generate additional movement information suitable for acceleration and enhancement of adequate sensorimotor representations and processible below the level of consciousness. In the experimental setting, participants were asked to learn a closed motor skill (technique acquisition of indoor rowing). One group was treated with visual information and two groups with audiovisual information (sonification vs. natural sounds). For all three groups learning became evident and remained stable. Participants treated with additional movement sonification showed better performance compared to both other groups. Results indicate that movement sonification enhances motor learning of a complex gross motor skill-even exceeding usually expected acoustic rhythmic effects on motor learning.

The effects of manipulated augmented sensory feedback on error detection when using a touch screen

The purpose of the present study was to determine which augmented sensory modality would best develop subjective error-detection capabilities of learners performing a spatial-temporal task when using a touch screen monitor. Participants were required to learn a 5-digit key-pressing task in a goal time of 2550 ms over 100 acquisition trials on a touch screen. Participants were randomized into 1 of 4 groups: 1) visual-feedback (colour change of button when selected), 2) auditory-feedback (click sound when button was selected), 3) visual-auditory feedback (both colour change and click sound when button was selected), and 4) no-feedback (no colour change or click sound when button was selected). Following each trial, participants were required to provide a subjective estimate regarding their performance time in relation to the actual time it took for them complete the 5-digit sequence. A no-KR retention test was conducted approximately 24-hours after the last completed acquisition trial. Results showed that practicing a timing task on a touch screen augmented with both visual and auditory information may have differentially impacted motor skill acquisition such that removal of one or both sources of augmented feedback did not result in a severe detriment to timing performance or error detection capabilities of the learner. The present study reflects the importance of multimodal augmented feedback conditions to maximize cognitive abilities for developing a stronger motor memory for subjective error-detection and correction capabilities.

Transition from an anti-phase error-correction-mode to a synchronization mode in the mutual hand tracking

Proactive motion in hand tracking and in finger bending, in which the body motion occurs prior to the reference signal, was reported by the preceding researchers when the target signals were shown to the subjects at relatively high speed or high frequencies. These phenomena indicate that the human sensory-motor system tends to choose an anticipatory mode rather than a reactive mode, when the target motion is relatively fast. The present research was undertaken to study what kind of mode appears in the sensory-motor system when two persons were asked to track the hand position of the partner with each other at various mean tracking frequency. The experimental results showed a transition from a mutual error-correction mode to a synchronization mode occurred in the same region of the tracking frequency with that of the transition from a reactive error-correction mode to a proactive anticipatory mode in the mechanical target tracking experiments. Present research indicated that synchronization of body motion occurred only when both of the pair subjects operated in a proactive anticipatory mode. We also presented mathematical models to explain the behavior of the error-correction mode and the synchronization mode.

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

Effective synchronization of a class of chua's chaotic systems using an exponential feedback coupling

A robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method. © 2013 Patrick Louodop et al.

Practical scheme for error control using feedback

We describe a scheme for quantum-error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols [for example, Ahn Phys. Rev. A 65, 042301 (2001)], is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit flips. We also consider implementation in a solid-state quantum-computation architecture and estimate the maximal error rate that could be corrected with current technology.

Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels

Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal. Copyright (C) 2009 Marcio Eisencraft et al.

Chaotic Synchronization in Discrete-Time Systems Connected by Bandlimited Channels

Due to the broadband characteristic of chaotic signals, many of the methods that have been proposed for synchronizing chaotic systems do not usually present a satisfactory performance when applied to bandlimited communication channels. Here, the effects of bandwidth limitations imposed by the channel on the synchronous solution of a discrete-time chaotic master-slave network are investigated. The discrete-time system considered in this study is the Henon map. It is analytically shown that synchronism can be achieved in such a network by introducing a digital filter in the feedback loop responsible for generating the chaotic signal that will be sent to the slave node. Numerical simulations relating the filter parameters, such as its order and cut-off frequency, to the maximum Lyapunov exponent of the master node, which determines if the transmitted signal is chaotic or not, are also presented. These results can be useful for practical communication schemes based on chaos.

Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber , Phys. Rev. Lett. 86, 4402 (2001)].

Controlling chaos in a Lorenz-like system using feedback

We demonstrate that the dynamics of an autonomous chaotic laser can be controlled to a periodic or steady state under self-synchronization. In general, past the chaos threshold the dependence of the laser output on feedback applied to the pump is submerged in the Lorenz-like chaotic pulsation. However there exist specific feedback delays that stabilize the chaos to periodic behavior or even steady state. The range of control depends critically on the feedback delay time and amplitude. Our experimental results are compared with the complex Lorenz equations which show good agreement.

Wireless GPS-based phase-locked synchronization system for outdoor environment.

Synchronization of data coming from different sources is of high importance in biomechanics to ensure reliable analyses. This synchronization can either be performed through hardware to obtain perfect matching of data, or post-processed digitally. Hardware synchronization can be achieved using trigger cables connecting different devices in many situations; however, this is often impractical, and sometimes impossible in outdoors situations. The aim of this paper is to describe a wireless system for outdoor use, allowing synchronization of different types of - potentially embedded and moving - devices. In this system, each synchronization device is composed of: (i) a GPS receiver (used as time reference), (ii) a radio transmitter, and (iii) a microcontroller. These components are used to provide synchronized trigger signals at the desired frequency to the measurement device connected. The synchronization devices communicate wirelessly, are very lightweight, battery-operated and thus very easy to set up. They are adaptable to every measurement device equipped with either trigger input or recording channel. The accuracy of the system was validated using an oscilloscope. The mean synchronization error was found to be 0.39 μs and pulses are generated with an accuracy of <2 μs. The system provides synchronization accuracy about two orders of magnitude better than commonly used post-processing methods, and does not suffer from any drift in trigger generation.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

Spatio-temporal Brain Dynamics Mediating Post-error Behavioral Adjustments.

Optimal behavior relies on flexible adaptation to environmental requirements, notably based on the detection of errors. The impact of error detection on subsequent behavior typically manifests as a slowing down of RTs following errors. Precisely how errors impact the processing of subsequent stimuli and in turn shape behavior remains unresolved. To address these questions, we used an auditory spatial go/no-go task where continual feedback informed participants of whether they were too slow. We contrasted auditory-evoked potentials to left-lateralized go and right no-go stimuli as a function of performance on the preceding go stimuli, generating a 2 × 2 design with "preceding performance" (fast hit [FH], slow hit [SH]) and stimulus type (go, no-go) as within-subject factors. SH trials yielded SH trials on the following trials more often than did FHs, supporting our assumption that SHs engaged effects similar to errors. Electrophysiologically, auditory-evoked potentials modulated topographically as a function of preceding performance 80-110 msec poststimulus onset and then as a function of stimulus type at 110-140 msec, indicative of changes in the underlying brain networks. Source estimations revealed a stronger activity of prefrontal regions to stimuli after successful than error trials, followed by a stronger response of parietal areas to the no-go than go stimuli. We interpret these results in terms of a shift from a fast automatic to a slow controlled form of inhibitory control induced by the detection of errors, manifesting during low-level integration of task-relevant features of subsequent stimuli, which in turn influences response speed.