This paper investigates the use of chaotic pulsewidth modulation (CPWM) scheme for electronic ballasts to eliminate visible striations (appearance of black and white bands along the lamp tube) in fluorescent lamps. As striations can be eliminated by superimposing a small amount of dc current or low frequency ac current to the electrodes to produce composite current waveform through the lamp, the underlying principle of this work is based on the fact that the power spectral density of the lamp current will be rich of low-frequency harmonics at the output of inverters switching with CPWM. Most importantly, the lamp life will not be affected with chaotic switchings, because the lamp current crest factor is found to be similar to the one with standard pulsewidth modulation (PWM) and the lamp current does not have dc component. The effectiveness of eliminating striations is confirmed experimentally with a T8 36W prototype.

We investigate the statistical features of both random- and chaos-based FM timing signals to ascertain their applicability to digital circuits and systems. To achieve such a goal, we consider both the case of single- and two-phase logic and characterize the random variable representing, respectively, the time lag between two subsequent rising edges or between two consecutive zero-crossing points of the modulated timing signal. In particular, we determine its probability density and compute its mean value and variance for cases which are relevant for reducing Electromagnetic emissions. Finally, we address the possible problems of performance degradation in a digital system driven by a modulated timing signal and to cope with this we give some guidelines for the proper choice of the statistical properties of the modulating signals.

This paper presents design of spreading codes for asynchronous DS-CDMA systems. We generate maximal-period sequences with negative auto-correlations based on one-dimensional maps with finite bits whose shapes are similar to piecewise linear chaotic maps. We propose an efficient search algorithm to find such maximal-period sequences. This algorithm makes it possible to find many kinds of maximal-period sequences with sufficiently long period for practical CDMA applications. We also report that maximal-period sequences can outperform conventional Gold sequences in terms of bit error rate (BER) in asynchronous DS-CDMA systems.

A performance comparison is developed between a chaotic communication system and a spread spectrum system with similar features in terms of bandwidth and transceiver structure but based on more conventional Gold sequences. Comparison is made in the presence of noise and multipath contributions which degrade the channel quality. It is shown that, because of its more favourable correlation properties, the chaotic scheme exhibits lower error rates, at a parity of the bandwidth expansion factor. The same favourable correlation properties are also used to explain and show, through a numerical example, the benefits of chaotic segments in a multi-user environment.

A number of schemes have been proposed for communication using chaos over the past years. Regardless of the exact modulation method used, the transmitted signal must go through a physical channel which undesirably introduces distortion to the signal and adds noise to it. The problem is particularly serious when coherent-based demodulation is used because the necessary process of chaos synchronization is difficult to implement in practice. This paper addresses the channel distortion problem and proposes a technique for channel equalization in chaos-based communication systems. The proposed equalization is realized by a modified recurrent neural network (RNN) incorporating a specific training (equalizing) algorithm. Computer simulations are used to demonstrate the performance of the proposed equalizer in chaos-based communication systems. The Henon map and Chua's circuit are used to generate chaotic signals. It is shown that the proposed RNN-based equalizer outperforms conventional equalizers.

The purpose of this study is to show the chaotic features of rhythmic joint movement. Depending on the experimental conditions, one (or both) elbow angle(s) was (were) measured by one (or two) goniometer(s). Pacing was provided for six different frequencies presented in random order. When the frequency of the pace increased, the fractal dimension and first Lyapunov exponent tended to increase. Moreover, the first Lyapunov exponent obtained positive values for all of the observed data. These results indicate that there is chaos in rhythmic joint movement and that the larger the frequency, the more chaotic the joint movement becomes.

Nonlinear feedback shift registers (NFSRs), which can generate maximal-period sequences called de Bruijn sequences, are regarded as one-dimensional maps with finite bits by observing states of the registers at each time. Such one-dimensional maps are similar to the Bernoulli map which is a famous chaotic map. This implies that an NFSR is one of finite-word-length approximations to the Bernoulli map. Inversely, constructing such one-dimensional maps with finite bits based on other chaotic maps, we can design new types of NFSRs, called extended NFSRs, which can generate new maximal-period sequences. We design such extended NFSRs based on some well-known chaotic maps, which gives a new concept in sequence design. Some properties of maximal-period sequences generated by such NFSRs are investigated and discussed.

A number of studies have recently been published concerning chaotic neuron models and asynchronous neural networks having chaotic neuron models. In the case of large-scale neural networks having chaotic neuron models, the neural network should be constructed using analog hardware, rather than by computer simulation via software, due to the high speed and high integration of analog circuits. In the present study, we discuss the circuit structure of a chaotic neuron model, which is constructed on the basis of the mathematical model of an asynchronous chaotic neuron. We show that the pulse-type hardware chaotic neuron model can be constructed on the basis of the mathematical model of an asynchronous chaotic neuron. The proposed model is an effective model for the cell body section of the pulse-type hardware chaotic neuron model for ICs. In addition, we show the bifurcation structure of our composed model, and discuss the bifurcation routes and return maps thereof.

In this paper, four coupled chaotic circuits generating four-phase quasi-synchronization of chaos are proposed. By tuning the coupling parameter, chaotic wandering over the phase states characterized by the four-phase synchronization occurs. In order to analyze chaotic wandering, dependent variables corresponding to phases of solutions in subcircuits are introduced. Combining the variables with hysteresis decision of the phase states enables statistical analysis of chaotic wandering.

The concept of stochastic association has originally been proposed in relation to single-electron devices having stochastic behavior due to quantum effects. Stochastic association is one of the promising concepts for future VLSI systems that exceed the conventional digital systems based on deterministic operation. This paper proposes a CMOS stochastic associative processor using PWM (pulse-width modulation) chaotic signals. The processor stochastically extracts one of the stored binary patterns depending on the order of similarity to the input. We confirms stochastic associative processing operation by experiments for digit pattern association using the CMOS test chip.

A self-similar behavior characterizes the traffic in many real-world communication networks. This traffic is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. The self-similar processes are identified by means of a polynomially decaying trend of the autocovariance function. In this work we concentrate on two criteria to build a chaotic system able to generate self-similar trajectories. The first criterion relates self-similarity with the polynomially decaying trend of the autocovariance function. The second one relates self-similarity with the heavy-tailedness of the distributions of the sojourn times in the ON and/or OFF states. A family of discrete-time chaotic systems is then devised among the countable piecewise affine Pseudo-Markov maps. These maps can be constructed so that the quantization of their trajectories emulates traffic processes with different Hurst parameters and average load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.

This paper deals with the approximation of multi-dimensional chaotic dynamics by using the multi-stage fuzzy inference system. The number of rules included in multi-stage fuzzy inference systems is remarkably smaller compared to conventional fuzzy inference systems where the number of rules are proportional to an exponential of the number of input variables. We also propose a method to optimize the shape of membership function and the appropriate selection of input variables based upon the genetic algorithm (GA). The method is applied to the approximation of typical multi-dimensional chaotic dynamics. By dividing the inference system into multiple stages, the total number of rules is sufficiently depressed compared to the single stage system. In each stage of inference only a portion of input variables are used as the input, and output of the stage is treated as an input to the next stage. To give better performance, the shape of the membership function of the inference rules is optimized by using the GA. Each individual corresponds to an inference system, and its fitness is defined by using the prediction error. Experimental results lead us to a relevant selection of the number of input variables and the number of stages by considering the computational cost and the requirement. Besides the GA in the optimization of membership function, we use the GA to determine the input variables and the number of input. The selection of input variable to each stage, and the number of stages are also discussed. The simulation study for multi-dimensional chaotic dynamics shows that the inference system gives better prediction compared to the prediction by the neural network.

In this paper we consider a tensor-based approach to the analytical computation of higher-order expectations of quantized trajectories generated by Piecewise Affine Markov (PWAM) maps. We formally derive closed-form expressions for expectations of trajectories generated by three families of maps, referred to as (n,t)-tailed shifts, (n,t)-broken identities and (n,t,π)-mixing permutations. These families produce expectations with asymptotic exponential decay whose detailed profile is controlled by map design. In the (n,t)-tailed shift case expectations are alternating in sign, in the (n,t)-broken identity case they are constant in sign, and the (n,t,π)-mixing permutation case they follow a dumped periodic trend.

This paper deals with the control of chaotic dynamics by using the approximated system equations which are obtained by using the Genetic Programming (GP). Well known OGY method utilizes already existing unstable orbits embedded in the chaotic attractor, and use linearlization of system equations and small perturbation for control. However, in the OGY method we need transition time to attain the control, and the noise included in the linealization of equations moves the orbit into unstable region again. In this paper we propose a control method which utilize the estimated system equations obtained by the GP so that the direct nonlinear control is applicable to the unstable orbit at any time. In the GP, the system equations are represented by parse trees and the performance (fitness) of each individual is defined as the inversion of the root mean square error between the observed data and the output of the system equation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. In the simulation study, the method is applied at first to the artificially generated chaotic dynamics such as the Logistic map and the Henon map. The error of approximation is evaluated based upon the prediction error. The effect of noise included in the time series on the approximation is also discussed. In our control, since the system equations are estimated, we only need to change the input incrementally so that the system moves to the stable region. By assuming the targeted dynamic system f(x(t)) with input u(t)=0 is estimated by using the GP (denoted (x(t))), then we impose the input u(t) so that xf=(t+1)=(x(t))+u(t) where xf is the fixed point. Then, the next state x(t+1) of targeted dynamic system f(x(t)) is replaced by x(t+1)+u(t). The control method is applied to the approximation and control of chaotic dynamics generating various time series and even noisy time series by using one dimensional and higher dimensional system. As a result, if the noise level is relatively large, the method of the paper provides better control compared to conventional OGY method.

This paper deals with the identification of system equation of the chaotic dynamics by using smaller number of data based upon the genetic programming (GP). The problem to estimate the system equation from the chaotic data is important to analyze the structure of dynamics in the fields such as the business and economics. Especially, for the prediction of chaotic dynamics, if the number of data is restricted, we can not use conventional numerical method such as the linear-reconstruction of attractors and the prediction by using the neural networks. In this paper we utilize an efficient method to identify the system equation by using the GP. In the GP, the performance (fitness) of each individual is defined as the inversion of the root mean square error of the spectrum obtained by the original and predicted time series to suppress the effect of the initial value of variables. Conventional GA (Genetic Algorithm) is combined to optimize the constants in equations and to select the primitives in the GP representation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. The crossover operation used here means the replacement of a part of tree in individual A by a part of tree in individual B. To avoid the meaningless genetic operation, the validity of prefix representation of the subtree to be embedded to the other tree is probed by using the stack count. These newly generated individuals replace old individuals with lower fitness. The mutation operation is also used to avoid the convergence to the local minimum. In the simulation study, the identification method is applied at first to the well known chaotic dynamics such as the Logistic map and the Henon map. Then, the method is applied to the identification of the chaotic data of various time series by using one dimensional and higher dimensional system. The result shows better prediction than conventional ones in cases where the number of data is small.

This paper describes an IC implementation of current-mode chaotic neuron circuit for the chaotic neural network. The chaotic neuron circuit which composes of a first generation switched-current integrator and a conventional current amplifier is fabricated in a standard 0.8 µ m CMOS technology. Experimental results of the chaotic neuron circuit reproduce the dynamical behavior of the chaotic neuron model.

Though considerable effort has recently been devoted to hardware realization of one-dimensional chaotic systems, the influence of implementation inaccuracies is often underestimated and limited to non-idealities in the non-linear map. Here we investigate the consequences of sample-and-hold errors. Two degrees of freedom in the design space are considered: the choice of the map and the sample-and-hold architecture. Current-mode systems based on Bernoulli Shift, on Tent Map and on Tailed Tent Map are taken into account and coupled with an order-one model of sample-and-hold to ascertain error causes and suggest implementation improvements.

A switched-current integrated circuit, which realizes the chaotic neuron model, is presented. The circuit mainly consists of CMOS inverters that are used as transconductance amplifiers and nonlinear elements. The chip was fabricated using a 1.2 µm HP CMOS process. A single neuron cell occupies only 0.0076 mm2, which represents an area smaller than the one occupied by a standard bonding pad. The circuit operation was tested at a clock frequency of 2 MHz.

Recently there have been several attempts to construct a Markov information source based on chaotic dynamics of the PLM (piecewise-linear-monotonic) onto maps. Study, however, soon informs us that Kalman's 1956 embedding of a Markov chain is to be highly appreciated. In this paper Kalman's procedure for embedding a prescribed Markov chain into chaotic dynamics of the PLM onto map is revisited and improved by using the PLM onto map with the minimum number of subintervals.

This paper presents a novel dead-beat synchronization scheme and applies it to communications in discrete-time chaotic systems. A well-known Henon system is considered as an illustrative example. In addition, a Henon-based image processing application effectively exploits the proposed scheme's effectiveness.