In this paper, we have studied an important class of first order differential equations with nonlinear delayed feedback. The nonlocal dynamics of such equations was investigated by analytical and numeric–analytical methods. An approach based on asymptotic analysis made it possible to study attractors consisting of impulse type solutions. We obtained some numerical characteristics of irregular oscillations and studied their dependence on the delay.

The statistical characteristics of the level crossing intervals of the chaotic process generated by the logistic map have been studied. In the previous works, the probability distributions P of the crossing intervals for this type of chaotic process have been derived only in the form of recursive expressions. In this paper the probability distributions p(0) and p(1) are studied by the help of Tent-map, and they are obtained in the form of explicit expressions, instead of recursive expressions. The numerical calculations for these quantities become simple and accurate.

In this paper we analyzed the statistical properties of the sum-lengths of the adjacent level crossing intervals of the chaotic process generated by the logistic map. We found a lot of new interesting phenomena and properties, which have never been observed in the past research of stationary random processes

Usually, sigma-delta modulators (/spl Sigma//spl Delta/M) are modeled by replacing the quantizer with an additive white noise source. Based on this linear model, linear decoder structures can be designed. However, the /spl Sigma//spl Delta/M is a nonlinear system, and corresponding nonlinear decoder structures may be able to achieve a better signal-to-quantization-noise ratio (SQNR) performance. In this paper, a new nonlinear decoding algorithm is presented. It is based on the projection onto complex sets (POCS) algorithm developed by Hein and Zakhor. Our algorithm reduces the decoding problem to the solution of a single quadratic programming problem based on the state equations of the modulator and the condition that the modulator input signal is bandlimited. The bandlimitation constraint is directly applied to the state equations. Thus, the resulting quadratic programming problem needs to be solved only once.

The design of spread spectrum clock generators usually is an iterative procedure. In the design loop efficient performance criteria are required to select an optimal generator. Usually the PDS is used to rate the EMI performance. However the use of PDS results in a very high calculation effort and speeds down the design loop. In contrast to classical EMI rating by use of the PDS we propose the use of simple statistical characteristics. We investigate the dependence between the EMI performance of the clock process, the statistical characteristics and different maps used for chaotic clock generation.

Spread spectrum clock signals are used in electronic devices to reduce the electromagnetic interference (EMI). In this paper we investigate clock signals with frequency or time interval modulation, by short length sequences of arbitrary waveform. The paper focuses on the viewpoints: 1) analyzing the EMI performance with regard to the IF bandwidth, defined by the EMC standard; and 2) considering application-specific restrictions of clock signal parameters such as frequency range or minimum on and off time. As an application example a DC-DC-converter is treated. The results are compared with modulating sequences generated by chaotic maps.

The behavioural analysis of hybrid systems is to a large extend an open problem. In this paper it is shown how the construction of an embedded map can be used to determine the characteristics of the output signal of a hybrid system. The method is demonstrated with two DC-DC converter examples.

Usually sigma-delta modulators (/spl Sigma//spl Delta/M) are modelled by replacing the quantizer with an additive white noise source. This linear modelling leads to decoder structures realizing approximately a linear rectangular filter. However, due to the low resolution quantizer the /spl Sigma//spl Delta/M is an inherently nonlinear system. This might mean that a nonlinear analysis could yield more effective decoder structures including better linear filters. In this paper a new linear filtering approach for decoder design is proposed. It achieves a decoding performance superior to rectangular filtering.

AbsfmcrThis paper treats the theory of chaotic point processes (chaotic event streams). Processes of this type appear in continuous-discrete or hybrid systems, which have become a topic of research in the last few years. The statistical analysis of chaotic point processes is interesting both from theoretical and practical points of view and important for practical applications in signal generation and power electronics. In this paper the basic model and the characteristics of point processes are provided. Then the paper discusses, how the statistical charmcteristics of the output signal of hybrid system can be calcutated. We demonstrate how the analysis results can be used. to solve the inverse problem statistical system design and control. The approach i s demonstrated with nunierous examples providing new statistical results in chaotic system design and control.

This paper treats the theory of chaotic point processes (chaotic event streams). Processes of this type appear in continuous-discrete or switching systems, which have become a topic of research in the last few years. The statistical analysis of chaotic point processes is interesting both from theoretical and practical points of view and important for practical applications in signal generation and power electronics. In this paper, the basic model and the characteristics of point processes are provided. A basic statistical analysis is carried out and demonstrated with some applications.

The paper presents a design-oriented analysis of dc-dc converters valid for both periodic and aperiodic operation. Bifurcation and statistical analysis are applied to a peak current mode controlled boost converter. The main. benefit of aperiodic (chaotic) converter operation-reduction of electromagnetic interference-is. discussed. Periodic and aperiodic behavior are compared. Periodic converter operation exhibits the smallest ripple waveform but the worst (purely discrete) spectrum. Aperiodic converter operation yields a broader spectrum but a larger ripple. Tradeoffs between ripple and spectrum for the practical use of chaotic dc-dc converters are suggested. The paper discusses the choice of the converter's bifurcation parameter from the ripple and spectrum points of view.

The paper applies statistical analysis to chaotic dc-dc converters. A boost converter under current-mode control using a duty cycle limiter is analyzed. A novel stroboscopic map including this limiter is presented. Properties of the converter's inductor current are expressed via the invariant density of the embedded stroboscopic map. The map governs an impulse process. The power density spectrum of this process is calculated and related to that of the inductor current. Expressions for the inductor current ripple and power density spectrum enable the simultaneous consideration of electromagnetic interference and ripple issues during an early design stage.

Variance analysis is used for the estimation of how random device parameter variation effects the behavior of analog integrated circuits. This method is very effective if the random parameter deviations can be assumed to be normally distributed and statistically independent and if the nonlinear dependence of the circuit characteristics can be linearized around the nominal (mean) parameter values. It is shown under which conditions the nonlinear dependencies of the system characteristics on the parameters have to be taken into account and how this can improve the accuracy of statistical analysis. This is illustrated with two examples: a transconductance amplifier and an analog filter.

This paper provides a comprehensive overview of chaotic communication methods and schemes with emphasis on digital schemes. Starting from general demands for communications, the general communication system structure is introduced. From this basic viewpoint, different classical and chaotic modulation and demodulation methods are treated and classified, For the performance analysis and comparison, a discrete-time statistical calculus is developed and applied to chaotic signal processing schemes. Discrete-time baseband models are developed, which are suitable for a statistical performance analysis. Analysis results for various example systems are provided and compared. New decoder structures arc proposed and included in the comparative studies.

In this paper, the authors present their opinion and research results collected during the last ten years on the conjunction of chaos and cryptography. Special consideration is taken to show some general critical points and limitations of this approach and to provide some pointers to a comprehensive and careful evaluation of the cryptographical properties of chaotic systems.

A case study is presented for the description and analysis of SigmaDelta-modulators based on evolution operators. In particular we derive the density operator and introduce the observation operators related to the quantized output signal, Based on that we demonstrate and discuss the implication of the operator analysis to optimal and suboptimal decoder design. As a vehicle the first order modulator with constant input signal is used throughout the paper.

This paper considers a class of switched dynamical systems to which two periodic inputs are applicable. We derive a one-dimensional (1-D) return map and its derivative analytically for arbitrary shapes of the inputs. Based on the derivative, we introduce a slope chart that displays the relationship between the slope of the return map and that of the inputs. Applying the slope chart to a simplified model of the buck-boost converter (SBBC) with two periodic triangular inputs, we obtain a sufficient condition for chaos generation and that for the stability of the periodic behavior. The conditions guarantee that the first input can cause chaotic or periodic behavior and that the second input can change from chaotic behavior into periodic behavior and vice versa. A circuit model of the system is also proposed and the periodic and chaotic behaviors are demonstrated in the laboratory

Recent publications on DC-DC converters have pointed out that a chaotic operation mode may be of advantage for EMC reasons. This paper proposes a boost-converter scheme the switching operation of which is controlled by a chaotic return map. A spectral analysis of the converter's input current demonstrates how the shape of the return map affects the power density spectrum of the input current. This provides an approach to solve the design problem, i.e. to choose a return map in order to meet particular spectral demands. Finally a simple circuit solution for the chaotic control of the converter is proposed.

We define two impulse sensitivity functions (ISF) describing the transient and the stationary effects of perturbations on the trajectory of oscillators. These functions give an insight into the sensitivity of the oscillator over time. They can be used to rate different oscillators according to their sensitivity to perturbations e.g. by noise. Both functions are derived from the properties of the corresponding dynamic system model and its monodromy matrix. The calculation of the ISF is shown and correlations between the nonlinearity contained in the oscillator and its noise behaviour is demonstrated by an example.