Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

Alapfokú nemlineáris hálózatelméleti ismeretek.

The study of nonlinear dynamics and chaotic behavior of electrical systems was started about ten years ago. Understanding of these phenomena explains many strange behaviors of electrical systems which cannot be predicted using the conventional theorems and design approaches. Moreover, the chaotic signals that are "noise-like" signals generated by a known deterministic system have many potential applications from measurement engineering to data transmission.

The main goal of this lecture is to discuss the nonlinear dynamics and chaotic behavior of electrical systems in detail and to survey the most important analysis tools applied in this field. The latest results in the field of chaotic communications are also presented. It will be shown that how the knowledge of chaotic signal generator can be exploited for noise and interference suppression. A chaotic wireless local area network WLAN being developed in the framework of the Esprit #31103 INSPECT EU Project will be discussed in detail. As an example the chaotic behavior of sampling and analog phase-locked loop is investigated and the behavior of a chaotic analog PLL is tested by laboratory measurements.

PART ONE: CHAOTIC SIGNAL GENERATION BY ANALOG AND SAMPLING PHASE-LOCKED LOOPS

• goals of chaotic signal generations
• operation of APLL and SPLL circuits
• development of baseband models

• SPLL: one-dimensional bifurcation diagram
• APLL: two-dimensional bifurcation diagram
• properties of generated chaotic signal
• stability of chaotic attractors

• circuit diagram and operation of chaotic APLL
• design of a chaotic APLL
• performance evaluation of generated chaotic signals by measurements

• basic definitions
• classification of dynamical systems
• continuous- and discrete-time dynamical systems
• existence and uniqueness of solution
• the flow
• examples

• wondering and nonwondering states
• limit points and limit sets
• attracting limit sets, attractors and basins of attraction
• equilibrium points and fixed points
• periodic, quasi-periodic and chaotic steady-state
• properties of chaotic attractors
• dimension of attracting limit sets
• classifications of attractors

• stability of equilibrium points
• eigenvalues, eigenvectors and eigenspaces
• manifolds
• homoclinic and heteroclinic orbits
• Poincaré map
• chaos in the sense of Shil'nikov
• Shil'nikov's theorem
• Lyapunov exponents
• classification of attracting limit sets

• basic definitions
• Hopf, saddle-node and period-doubling bifurcations
• routes to chaos: period-doubling, intermittency and torus breakdown
• bifurcation diagrams
• parameter space diagram

• channel model
• performance measures
• orthonormal basis functions and M-ary modulation schemes
• coherent and noncoherent receivers
• role of synchronization

• advantages of and typical applications for wideband data communications
• conventional approaches
• usage of chaotic carriers

• chaotic modulation techniques
• multilevel modulation using one or more chaotic basis functions
• CSK: demodulation by means of synchronization
• implementation of chaotic synchronization
• COOK, DCSK and FM-DCSK: demodulation without synchronization

• performance measures of chaotic communications systems
• development of low-frequency equivalent model
• stationarity of chaotic signals
• effect of symbol duration
• performance evaluation of CSK, COOK, DCSK and FM-DCSK transceivers

• noise and interference suppression by optimization
• design of cost function
• application of noise and interference suppression to the DCSK modulation scheme

• survey of WLAN data communications systems
• development of the INSPECT WLAN FM–DCSK system
• performance evaluation

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