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Engineering, 2012, 4, 177-178 http://dx.doi.org/10.4236/eng.2012.44023 Published Online April 2012 (http://www.SciRP.org/journal/eng) Review of the Boo k “ No n-Traditional Dynami cs: Theory and Practice” Gennadiy G. Goshin Tomsk State University of Control Systems and Radio Electronics, Tomsk-City, Russia Email: smolskiysm@mail.ru Received February 20, 2012; revised March 20, 2012; accepted March 28, 2012 ISBN: 978-1-935068-57-0 237 pp Pub.Date: October/2011 Price: $89 The offered book is devoted to theoretical and applied problems of nonlinear dynamics of radio physical sys- tems. The main goal of this book is theoretical and expe- rimental investigations of key principles and laws of ra- dio physical system’s functioning with continuous and discrete time, in which both regular and chaotic oscilla- tion types may occur. Modern radio physics and radio engineering, as it fol- lows from scientific publications, feels the increased ne- cessity in the sources of wide-band noise-like o scillation s. This necessity is caused by possibility to create on this basis the systems of electronic counter measures and ra- dio masking, the noise-like radar technology and confi- dential communications, ultra-fast radio communications, cryptographic structures, devices for non-traditional in- teraction on biologic objects, various devices of special applications. All this is evidence of the fact that investi- gations directed to examination of dynamic instabilities and the determined chaos are quite relevant. Therefore, the urgency of this book and its practical significance cannot present any doubts. The book consists of six chapters. The first chapter is devoted to the mathematical model of non-autonomous oscillating system contained the nonlinear capacitor and having the four-dimension phase space. Numerical in- vestigation is conducted for bifurcation phenomena and processes occurring at variations of amplitude and fre- quency of the external force. It is proved that in the phase space of the system under investigation both strange cha- otic attractors and the strange non -chaotic attractors exist. Numerical results are confirmed by the full-scale ex- periments. The typical features of transition fro m regular types of oscillations to chaotic on es in the self-oscillating systems of oscillator and relaxation types are discussed in the second chapter. It is proved that fo r definite type of these systems non-linearity the chaotization of motions hap- pens according to one auto-parametric scenario. Numeri- cal results are confirmed by experimental results fulfilled on the basis of radio physical oscillating systems. The new spectral-temporal method for the analysis of oscillating systems is discussed in the third chapter. Pe- culiarities of construction of the mathematical model suitable for physical analysis are discussed, which de- scribe motions in the discrete and distributed dynamical systems. It is shown that if such systems are physically realizable, the processes in them can be described by identical systems of spectral-time equations. The compa- rative analysis is executed for natural fluctuations of os- cillating systems with delay and Thomson-type. The di- rect approach of spectrum calculation of Lyapunov char- acteristic exponents for systems with delayed feedback. Boundaries and the attraction basin of the time series attractor caused by modified logistic map are determined in the fourth chapter. Values of the control parameter, which divide regular chaotic types of oscillations and strictly-chaotic ones are found out. It is shown that at arising of the chaotic motion the control parameter be- havior corresponds to the phase transition of the second C opyright © 2012 SciRes. ENG G. G. GOSHIN 178 kind. The connection between considered map with the physical system with delayed feedback, which has the in- finite dimension of the phase space, is proved. Properties of modified logistic map are investigated analytically and numerically. A series of algorithms of noisy sequence generation with accurately predicted statistical characteristics is sug- gested. The nonlinear dynamics of two coupled modified logistic maps is examined. Bifurcation phenomena and processes are studied in detail. Two unknown earlier phe- nomena are described. The first one is arising the “inter- mittent synchronization” of two chaotic processes. The second one is formation in the phase space the geometri- cally ordered structures at strictly positive value of the Kolmogorov- Sinay entropy. Promising directions of UHF generating structures having high and uniform spectral density in the wide fre- quency range are investigated in the fifth chapter. The possible methods of such system constructions are ana- lyzed. On the basis of the last achievements of nonlinear chaotic dynamics, the variant of creation the source of the determined chaotic oscillations is offered intended for angular modulation of quasi-sinusoidal oscillator of UHF range. Numerical modeling results as well as results of physical experiments are discussed. A series of issues of robust systems for confidential communication with the chaotic carrier frequency is examined. New principles of double-channel syste ms with active and passive synchro- nization are described. The investigation results fort fre- quency-modulated systems of chaotic communication are given. Some problems, in which the mutual understanding of experts working in the field of nonlinear dynamics is absent , are investigat ed in the si xth chapter . To eliminate a series of ambiguities, authors offer the classification of physical systems, objects and processes based on attrac- tion the concept of an openness degree and the repro- duced motion type. Th e influence of the white noise with normal and uniform distribution laws upon dynamics of the quasi-periodic excited system is determined. The unambiguous correspondence between the sign of Lya- punov characteristic exponent and essential dependence of phase trajectory behavior upon initial conditions. Im- possibility of generation of Poisson pulse flows and the dynamic chaos by signing correlator of two sinusoidal processes with irrationally coupled frequencies is shown theoretically and experimentally. Scientific novelty of this book’s results consists in the following. 1) For the first time the mathematical model adequ- ately describing processes in oscillating system with four- dimension phase space and the nonlinear capacitor, which is under influence the external harmonic force; this mo- del allows determination of complicated dynamic modes, transitions into chaotic states, to prove the existence of rough attractors having fractal geometrical structures at the absence of positive Lyapunov exponen ts. 2) Requirements to frequency responses of linear cir- cuits and to a form of non-linearity are formed, which are the necessary conditions of autoparametric scenario of motion chaotization in the oscillating systems, the physi- cal sense of the scenario is stated. 3) Conditions are formulated, at which motions in lin- ear and nonlinear discrete and continuous systems may be described by a system of spectral-temporal equations. 4) The direct algorithm of calculation of the complete spectrum of characteristic Lyapunov exponen ts is offered for dynamic systems with delay. 5) Bifurcation phenomena and processes typical for a system of two coupled modified logistic maps are exam- ined. The new phenomena of synchronization of chaotic motions, of intermittent synchronization and arising of geometrically ordered structures in the phase space with the positive value of the Kolmogorov-Sinay entropy are discovered and investigated. 6) The white noise influence on dynamics of the non- linear dynamic systems with quasi-periodic excitation is examined. Practical significance of the book is determined by the fact that results obtained can be the basis of designing of microprocessor systems, digital automatons, combined circuits, which in combination with digital-analog con- verters and frequency (phase) modulators permit to solve the problem of creation of wide-band noise-type oscilla- tion sources. Results allow creation of generation algo- rithms of the white noise with normal and uniform dis- tribution laws and chaotic sequences with necessary va- lue of metric entropy. The book has the internal unity caused by it contents, structure and statement logic. Scientific issues and con- clusions are reasonable. Book materials are expounded clearly and correctly. My opinion is: this book is acco m- plished scientific investigation and its results may be evaluated as new large-scale scientific achievement in the field of nonlinear dynamics of electronic systems. REFERENCES [1] S. N. Vladimirov and S. M. Smolsky, “Non-Traditional Dynamics in Electronic: Theory and Practice,” Scientific Research Publishing, USA, 2011. To order: http://www.scirp.org/book/ Email: bookorder@scirp.org Copyright © 2012 SciRes. ENG |