Non-traditional Dynamics in Electronics: Theory and Practice

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Non-traditional Dynamics in Electronics: Theory and Practice E-Book

ISBN: 978-1-935068-57-0

237pp Pub. Date: October/2011

Scientific Research Publishing

Category: Physics & Mathematics

Price: $100

Full Text: View full text in PDF format

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Table of Contents
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The main theme of the proposed book is devoted to investigation of non-trivial problems of functioning of Ultra-High-Frequency (UHF) electronic devices and systems in the various type dynamic instability modes. Both flows and maps (representations) are considered because the relation between maps and flows was repeatedly discussed in different publications. On the contrary, all systems described in the offered book for the first time are considered from the point of view either internal structure, or the description and analysis.

Table of Contents
Chapter 1. Nonlinear-Parametric Effects and a Dynamic Chaos
1.1. Opening remarks
1.2. Mathematical model construction of the general type
1.3. Mathematical model in the resonance case
1.4. Numerical analysis results for the mathematical model
1.5. Estimation of Lyapunov dimension of the attractor
1.6. Physical experiment (variation of an external force amplitude)
1.7. Bifurcation processes’ investigation at variations of the external force frequency. Numerical and
full-scale experiments
1.8. Key results and conclusions
Chapter 2. Autoparametric Scenario of Motion Chaotization of Self-Oscillating Systems
2.1. Opening remarks
2.2. Necessary conditions of realization of an auto-parametric transition
to chaotic type of motion and the concomitant characters
2.3. Discussion on fulfillment condition holding of the numerical modeling
and the full-scale experiments
2.4. Realization of auto-parametric scenario in self-oscillating systems
2.4.1. Bifurcation processes in the system of relaxation type
 Development of the mathematical model its properties’ discussion
 Numerical modeling
 Physical experiment
2.4.2. Bifurcation processes in the self-oscillating system of oscillation type
 Construction of the mathematical model and discussion of its properties
 Numerical modeling
 Physical experiment
2.4.3. Bifurcations in the self-oscillation system with delay
 Development of the mathematical model and discussion of its properties
 Numerical modeling
 Physical experiment
2.5. Key results and conclusions
Chapter 3. Spectral-Time Expansion of Motion Equations of Discrete and Distributed Systems
3.1. Opening remarks
3.2. Development of mathematical models of oscillating structures with delay
3.2.1. The self-oscillating system of circular type
3.2.2. The self-oscillating system with negative resistance
3.3. Key prerequisites for development the system of spectral-time equations
3.4. The spectral-time method for analysis of SOS with DF, which mathematical
model is the nonlinear integral equation
3.5. Solution of Cauchy problem for the mathematical model in the form of
differential-difference equation of a neutral type
3.6. Reduction of the spectral-time equation system to the real form
3.7. About adaptability of asymptotic methods of the oscillation theory to the system
of spectral-time equations
3.8. About connection between the spectral-time description in two classes of SOS
3.9. About peculiarities of motion in dynamic systems with delay
3.10. Research of excitation regulations in SOS with DF
3.10.1 Determination of excitation areas by means of the D-fragmentation
method for the parameter space
3.10.2 Calculation of linear basis components for SOS with the pass-band filter
3.11. Delay influence on the natural fluctuation intensity of an amplitude and
a phase in SOS with DF
3.12. Polyharmonic processes in SOS with DF
3.12.1. Investigation of two-frequency oscillating modes on the basis of
averaged motion equations
3.12.2. Comparative analysis of exact and approximate solutions for two-frequency motions
3.12.3. Spectral characteristics of two-frequency mode. Full-scale experiment
3.13. Direct algorithm for calculation the spectrum of characteristic Lyapunov
exponents of the dynamic system with delay
3.13.1. Derivation of the disturbance evolution equation
3.13.2. The spectral-time expansion of the disturbance evolution equation
3.13.3. Limit transition to the nonlinear Van-der-Pole oscillator
3.13.4. Reduction to the finite-dimension system of equations
3.13.5. Algorithm testing
3.14. Key results and conclusions
Chapter 4. A Dynamic Chaos in Systems with Discrete Time
4.1. Opening remarks
4.2. The modified logistic map and its properties
4.2.1 Fixed points of maps, attractor boundaries and the basin of attraction
4.2.2 Bifurcation and spectral analysis of the time series generated by the map
4.2.3 The chaos and the strict chaos in MLM
4.2.4 Comparison of MLM with the self-oscillating system with the delayed feedback
4.2.5 Statistical map properties
4.3. Kolmogorov-Sinay entropy of MLM for the parametric external impact
4.3.1 Harmonic modulation of the order parameter
4.3.2 Modulation by the irregular process—the white noise
4.4. Bifurcation phenomena and processes in the system of coupled MLM
4.4.1 The mathematical model
4.4.2 The spectrum of Lyapunov exponents of the system of coupled MLM
4.4.3 Bifurcation analysis
4.4.4 The regular and chaotic synchronization
4.4.5 Formation of geometrically ordered structure on the phase space
4.5. Key results and conclusions
Chapter 5. A Dynamic Chaos in Applied Problems of Radio Electronics
5.1. Opening remarks
5.2. The wide-band generating structure of the UHF range with a high output spectral density
5.2.1. The mathematical model of the chaotic modulator
5.2.2. Numerical investigation of the chaotic attractor model
5.2.3. Practical implementation of the modulator
5.2.4. Experimental investigation of the modulator
5.2.5. Results of experiments in the UHF range
5.3. A dynamic chaos and confidential communication
5.3.1 Classification of communication systems using a dynamic chaos
5.3.2 Comparative analysis of some systems of synchronous chaotic communication
 The structure of considered systems of synchronous chaotic communication
 Investigation of the mathematical model of a chaotic oscillator
 Practical implementation of the chaotic oscillator
 Experimental investigations
5.3.3 Chaotic communication system with frequency modulation
5.3.4 The double-channel system of the active synchronous chaotic communication
5.3.5 The system of synchronous chaotic communication with passive synchronization
5.4. Key results and conclusions
Chapter 6. Ambiguous and Debatable Issues. Discussion, Search of Overcome Ways
6.1. Opening remarks
6.2. Classification of systems, objects, and processes
6.2.1 The closed dynamic system with a deterministic chaos
6.2.2 The closed locally-unstable dynamic system with regular behavior
6.2.3 The open conditionally-dynamic system. The quasi-deterministic chaos
6.2.4 The open conditionally-dynamic system. The induced chaos
6.3. Characteristic Lyapunov exponents and the sensitivity to initial conditions of the
quasi-periodically excited system with the white noise
6.3.1 The mathematical model of the analyzed system
6.3.2 An approach for fulfillment of numerical experiments
6.3.3 The white noise influence on the behavior of Lyapunov exponents
6.3.4 The white noise influence on essential dependence of phase
trajectories upon initial conditions
6.4. Does the sign correlation of quasi-periodic oscillation with the irrationally
correlated frequencies generate the deterministic chaos?
6.4.1 Brief statement of the main ideas of the publication under investigation
6.4.2 Analysis of publication results
6.4.3 Does the sign correlation give birth to the Poissonian flow?
6.4.4 Does the sign correlation give birth to the dynamic chaos?
6.4.5 The full-scale experiment
6.5. Key results and conclusions
CONCLUSIONS
REFERENCES
ABBREVIATIONS