Engineering, 2012, 4, 177-178 Published Online April 2012 (
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
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-
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
opyright © 2012 SciRes. ENG
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
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
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
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
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.
[1] S. N. Vladimirov and S. M. Smolsky, “Non-Traditional
Dynamics in Electronic: Theory and Practice,” Scientific
Research Publishing, USA, 2011.
To order:
Copyright © 2012 SciRes. ENG