This paper presents a review of up-to-date concepts of electronic chaos generators. Strategies for controlling chaotic behavior in various aspects are presented. We discus the applicability of various generators drawing attention to covered frequency range and possibilities of designing (control/shaping) of the spectral characteristics. Further, some of the existing methods for chaos control and for converting an unwanted chaotic behavior into a desirable mode of operation are discussed. These methods are later used in signal processing tasks related with chaos control techniques; namely coding of chaotic trajectories, information storage and retrieval, signal coding and compression. Finally we present some of the latest developments in the design and control of chaotic circuits for communication.
While in electronic systems there are many theoretical and experimental results on self- synchronization, optical chaotic signal synchronization is still an open field of research. Recently, we have proposed an optoelectronic infinite-dimensional dynamical system capable of chaotic self-synchronization. In this paper, experimental evidence of synchronization of chaotic modulated intensity lightwaves is shown to be effective in such a system. Moreover, we show that the theoretical model based on coupled delay-differential equations predicts waveforms that are at least qualitatively in good agreement with the measurements.
We investigate a number of phenomena which occur in synchronization in coupled or driven chaotic systems and which can cause difficulties in attaining synchronized states. We present direct experimental and numerical evidence for riddled basins of attraction, bursting phenomena, short wavelength bifurcations and size desynchronization effects. We show that typical Lyapunov stability exponents are not the optimal guide in designing such systems.
We show a new type of synchronization in coupled chaotic systems. We introduce the concept of monotonic stability for which all perturbations decay monotonically and describe the transition from a monotonically stable to asymptotically stable chaotic attractor. Application of monotonic synchronization for secure communication systems is also discussed.
In this paper a new approach to the parameter identification of nonlinear dynamic circuits is proposed. It is based on the concept of synchronization of nonlinear circuits and, in particular, on the Pecora-Carroll system decomposition and cascaded synchronization techniques. Moreover, the new identification procedure is formulated as an optimization problem and it is faced via a genetic algorithm. The introduction algorithm is applied to the famous Chua's oscillator, known for its rich variety of chaotic dynamics and bifurcations. Some examples, referring to different attractors, are reported.
A voltage-mode CMOS looped circuit generates complex chaos time series, and it is digitized by an AD converter. The digitized time series of internal state shows an irreversible multiple complexity in the past, due to bifurcation. The multiple complexity of internal states in chaos time series is utilized as a scramble code in a digital ciphering system. A binary coded information is bit-serially converted into a corresponding scramble code. An average conversion rate of the ciphering system using 8-bit data base is 102 k bit/sec. On the other hand, the internal states in the future time series are quite deterministic, even if it has multiple internal states in the past. The scramble code can be decoded by the deterministic phenomenon.
The utilization of the Henon map for chaotic-based data communication is investigated. The data is impressed on the mapping parameters and an inverse mapping is exploited for data recovery. The link performance is investigated in the presence of additive white Gaussian noise and techniques to enhance the performance are introduced and evaluated. Data security issues are investigated and original results are presented demonstrating that embedding techniques and radial basis functions do not predict the next unmodulated chaotic sample with the degree of accuracy required to decode a modulated signal. It is concluded that this form of chaotic modulation can find numerous applications when data security and privacy are of concern.
Two types of balanced binary sequence have recently been defined, referred to as a chaotic threshold sequence and a chaotic bit sequence, each of which is obtained from chaotic real- valued orbits generated by nonlinear maps. This paper presents a stream cipher system whose running-key sequences are threshold and bit sequences generated by Chebyshev polynomials. Such a system has the following characteristics: (1) Chebyshev threshold and bit sequences can easily generate unpredictable i.i.d. binary random variables; (2) The correlation properties of ciphertexts are at least as good as those of the standard block ciphers, DES and FEAL. Since portable ANSI C permits us to implement such a cipher system in the floating-point environment, Chebyshev threshold and bit sequences are excellent choices for running-key sequences in stream cipher cryptography.
This paper reports the first experimental verification of chaotic encryption of audio signals using integrated circuits. It is based on a gm-C modulator/demodulator analog CMOS IC that implements a 3rd-order nonlinear differential equation. This has been fabricated in 2.4 micrometer double-poly technology and includes on-chip tuning circuitry based on amplitude detection. It is capable of generating controllable continuous-time chaotic signals. Also, measurements demonstrate how to exploit the synchronization between two of them for encrypted transmission. In these experiments, the worst-case signal to noise ratio of the recovered signal is greater than +40 dB (at the low corner of the audio spectrum) with less than -0.2 dB loss of the input signal power. At higher frequencies, the signal-to- noise ratio rises up to +60 dB, while retaining similar losses at the receiver.
In this paper, we first demonstrate that the dynamics of the archetypal chaotic system based on the sawtooth map have a natural interpretation as noncausally filtered Bernoulli noise. This result is then extended to introduce an entire family of anticausal filters which can produce chaotic (deterministic) behavior. Finally, replacing the Bernoulli noise source with a feedback shift register and truncating the impulse response of the filters results in pseudo-chaos: colored pseudo-noise. By relying on feedback shift registers, pseudo-chaotic implementations avoid the drawbacks of conventional synthetic chaotic behavior. In fact, pseudo-chaos can produce behavior indistinguishable from true chaos under any finite level of scrutiny. However, as potential spreading codes in direct-sequence spread-spectrum applications, we argue that pseudo-chaotic sequences have few, if any, advantages over other forms of transformed pseudo-noise.
In contrast with almost all existing chaos communication techniques which are based on synchronization, we propose a communication system, whose principle relies on stochastical properties of chaotic signals. A key issue of this approach is that different chaotic systems can possess different auto-correlation functions (ACFs). We discuss how these properties can be exploited in order to detect on the receiver side, whether a certain chaotic signal is 'on air' or not. Thus, we describe a binary communication system, which possesses some common properties of conventional spread spectrum techniques since chaotic signals behave 'noise-like' and occupy an entire frequency band. Like conventional spread spectrum techniques the proposed chaos communication system allows multiple users to share the same band and it is also robust to channel influences. The motivations of using chaotic, nonrepeating carrier signals are: (1) the transmission possess a higher level of security than techniques using periodical carriers. (2) In contrast with conventional spread spectrum techniques neither acquisition nor tracking units are necessary for detection. (3) We expect less interference problems between different channel users.
Chaotic modulation has recently been proposed as an alternative to the conventional spread spectrum and code division multiple access system. It uses a chaotic dynamical system to modulate the signal of transmission by embedding it in the bifurcating parameter. The transmitted signal then occupies a wide bandwidth as desired. One advantage of this chaotic modulation communication is that it does not require synchronization which is a complicated procedure for a conventional SS system. The main difficulty of the chaotic modulation technique is to design a reliable receiver so that the signal of transmission can be demodulated after passing through a noisy channel. In this paper, adaptive filters are used for chaotic demodulation, that is, to estimate the signal of transmission in an on-line fashion. The two widely used adaptive filtering algorithms: least mean square (LMS) and recursive least square (RLS), are considered. Based on simulation, both LMS and RLS receivers are demonstrated to be more accurate than the inversion approach in the noisy environment.
In this paper it is shown that the extra ordinary amplification and high sensitivity of the regenerative detector is caused by the chaotic behavior of the system during operation. The detector was invented by Armstrong in 1922. We demonstrate the chaotic behavior using computer simulations. It is shown that during the period in which the irregularities appear, the amplification of incoming signals is maximal.
We show how it is possible to exploit a priori knowledge of the nonlinear dynamics of a system. Given a signal produced by a system, we first identify the parameters of the system and second we code sub-intervals of the signal into initial state-space points of the identified system. As a result of this method a whole waveform is coded as a sequence of points in state- space, a sequence of interval durations and a system of ordinary differential equations. We test these concepts on a challenging example in which the signal to be coded and compressed is produced by a chaotic oscillator.
This paper presents a novel chaotic coding scheme for correlated band-limited source signals. Two low implementation non-linear difference equations are introduced that exhibit chaotic properties within the confines of a specific modulating range. The two chaotic maps demonstrate the spectral conditioning effects of the modulation regime and highlight the robust noise-whitening properties over limited perturbation ranges. The performance of the novel strategy is then evaluated for noise-free circuits and existing echo cancellation technology shown to be optimized.
Digital chaotic behavior in an optically processing element is analyzed. It was obtained as the result of processing two fixed trains of bits. The process is performed with an optically programmable logic gate. Possible outputs, for some specific conditions of the circuit, are given. Digital chaotic behavior is obtained, by using a feedback configuration. Different ways to analyze a digital chaotic signal are presented.
One problem with using chaotic synchronization to communicate is that the response system is nonlinear, so that any variation in the amplitude of the chaotic driving signal degrades synchronization of the response system to the drive system. In this work it is shown that it is possible to design a response system that reproduces a scaled version of the chaotic driving signal when the drive signal is attenuated or amplified. A simple communications system is demonstrated to show that this type of synchronization is useful, and the effects of noise on the communications system are studied.
This research applies novel nonlinear signal detection techniques in studies of human subjects with respiratory and cardiac diseases. One of the studies concerns a breathing disorder during sleep, a disease called Obstructive Sleep Apnea (OSA). In a second study we investigate a disease of the heart, Atrial Fibrillation (AF). The former study involves nonlinear processing of the time sequences of sleep apnea recordings (cardio-respirograms) collected from patients with known obstructive sleep apnea, and from a normal control. In the latter study, we apply similar nonlinear metrics to Doppler flow measurements obtained by transesophageal echocardiography (TEE). One of our metrics, the 'chaotic radius' is used for tracking the position of points in phase space relative to some reference position. A second metric, the 'differential radius' provides a measure of the separation rate of contiguous (evolving) points in phase space. A third metric, the 'chaotic frequency' gives angular position of the phase space orbit as a function of time. All are useful for identifying change of physiologic condition that is not always apparent using conventional methods.
Conditions for the occurrence of generalized synchronization of unidirectionally coupled dynamical systems are given in terms of asymptotic stability. All theoretical results are illustrated by analytical and numerical examples.