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E-book: Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering

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This book contains a collection of recent advanced contributions in the field of nonlinear dynamics and synchronization, including selected applications in the area of theoretical electrical engineering. The present book is divided into twenty-one chapters grouped in five parts. The first part focuses on theoretical issues related to chaos and synchronization and their potential applications in mechanics, transportation, communication and security. The second part handles dynamic systems modelling and simulation with special applications to real physical systems and phenomena. The third part discusses some fundamentals of electromagnetics (EM) and addresses the modelling and simulation in some real physical electromagnetic scenarios. The fourth part mainly addresses stability concerns. Finally, the last part assembles some sample applications in the area of optimization, data mining, pattern recognition and image processing.

Part I Theory of Chaos and Synchronization and Applications in Mechanics, Transportation, Communication and Security Related System Concepts
1 Synchronization of Two Nonidentical Clocks: What Huygens Was Able to Observe?
3(16)
Krzysztof Czolczynski
Przemysaw Perlikowski
Andrzej Stefanski
Tomasz Kapitaniak
1.1 Introduction
3(2)
1.2 Model
5(2)
1.3 Energy Balance
7(2)
1.3.1 Energy Balance of the Pendulum
7(1)
1.3.2 Energy Balance of the Beam and Whole System (1,2)
8(1)
1.4 Numerical Results
9(5)
1.4.1 From Complete to (Almost) Antiphase Synchronization
9(2)
1.4.2 From Complete Synchronization to Quasiperiodic Oscillations
11(1)
1.4.3 From Antiphase to Almost-Antiphase Synchronization
12(1)
1.4.4 From Antiphase Synchronization to Quasiperiodic Oscillations
13(1)
1.5 From Complete to (Almost) Antiphase Synchronization
14(5)
References
17(2)
2 On the Synchronization of 1D and 2D Multi-scroll Chaotic Oscillators
19(22)
J.M. Munoz-Pacheco
E. Zambrano-Serrano
O.G. Felix-Beltran
E. Tlelo-Cuautle
L.C. Gomez-Pavon
R. Trejo-Guerra
A. Luis-Ramos
C. Sanchez-Lopez
2.1 Introduction
20(3)
2.2 General Aspects for the Amplifiers-Based Design of Chaotic Oscillators
23(2)
2.2.1 High-Level Modeling
23(1)
2.2.2 Opamp-Based Circuit Synthesis
24(1)
2.3 Hamiltonian-Based Synchronization of Multi-directional Multi-scroll Chaotic Oscillators
25(8)
2.3.1 Synchronization of 2D-4-Scroll Chaos Generators
27(2)
2.3.2 Synchronization of 3D-4-Scroll Chaos Generators
29(1)
2.3.3 Numerical Simulation Results
30(3)
2.4 Design of Chaos-Based Encrypted Communication Schemes
33(5)
2.4.1 Binary Transmission
34(1)
2.4.2 Analog Transmission
35(3)
2.5 Conclusions
38(3)
References
38(3)
3 Nonlinear Filtering of Chaos for Real Time Applications
41(20)
V. Kontorovich
Z. Lovtchikova
3.1 Introduction
41(1)
3.2 Chaotic Modelling of Random Signals
42(7)
3.2.1 Approximations for PDF of Strange Attractors
43(3)
3.2.2 Degenerated Cumulant Equations for Two-Moment Cumulants
46(3)
3.3 Filtering of Chaotic Signals in Presence of Additive Gaussian Noise
49(7)
3.3.1 Markov Theory of Non-linear Filtering
49(2)
3.3.2 Approximate Algorithms of Non-linear Filtering of Chaos
51(3)
3.3.3 Comparative Analysis of Nonlinear Filtering Approach
54(2)
3.4 "Multi-moment" Nonlinear Filtering of Chaos
56(5)
References
58(3)
4 Time-of-Flight Estimation Using Synchronized Chaotic Systems
61(20)
Christian F. Wallinger
Markus Brandner
4.1 Introduction
61(2)
4.1.1 Time-of-Flight Measurements
62(1)
4.1.2 Outline
63(1)
4.2 Synchronized Chaotic Systems
63(10)
4.2.1 Convergence
64(1)
4.2.2 Detection Range
65(1)
4.2.3 Discretization Algorithms and Numerical Issues
66(3)
4.2.4 Delay Estimators
69(4)
4.3 Experiments
73(5)
4.3.1 Different Window Lengths
73(2)
4.3.2 Different Noise Levels
75(1)
4.3.3 Different Orders of Numerical Solver
75(3)
4.4 Summary and Conclusions
78(3)
References
78(3)
5 Binary Synchronization of Complex Dynamics in Cellular Automata and its Applications in Compressed Sensing and Cryptography
81(16)
Radu Dogaru
Ioana Dogaru
5.1 Introduction and Motivation
81(3)
5.2 Automata Network Models and the Key Space
84(2)
5.3 Characterizing Complex Dynamics in Automata
86(3)
5.4 FPGA Implementations of Cellular Automata
89(1)
5.5 Applications
90(2)
5.5.1 Compressed Sensing Based on Chaotic Scan
90(1)
5.5.2 Efficient Generation of Spreading Sequences
91(1)
5.6 Conclusions
92(5)
References
94(3)
6 Self-Shaping Attractors for Coupled Limit Cycle Oscillators
97(22)
Julio Rodriguez
Max-Olivier Hongler
Philippe Blanchard
6.1 Introduction
97(2)
6.2 Networks of Mixed Canonical-Dissipative (MCD) Systems with Adpating Parameters
99(7)
6.2.1 Local Dynamics: L
99(1)
6.2.2 Coupling Dynamics: Ck
100(1)
6.2.3 Parametric Dynamics: Pk
100(6)
6.3 Dynamics of the Network
106(2)
6.3.1 Network of Ellipsoidal Hopf Oscillators
108(1)
6.4 Numerical Simulations
108(6)
6.4.1 Ellipsoidal Hopf Oscillators
109(1)
6.4.2 Cassini Oscillators
109(3)
6.4.3 Mathews-Lakshmanan Oscillators
112(2)
6.5 Conclusions and Perspectives
114(5)
References
115(4)
Part II Systems' Dynamics Modeling and Simulation with Applications to Real Physical Systems and Phenomena
7 Fast Switching Behavior in Nonlinear Electronic Circuits: A Geometric Approach
119(18)
Tina Thiessen
Soren Plonnigs
Wolfgang Mathis
7.1 Introduction and Motivation
119(2)
7.2 Geometric Approach of Circuits and Fast Switching Behavior
121(2)
7.2.1 Singular Points and Jumps
122(1)
7.3 Chart Representation of Circuits and Jump Phenomena
123(4)
7.3.1 Jumps in State Space
123(2)
7.3.2 Determining the State Space
125(1)
7.3.3 Transient Solution and Hit Point Calculation
126(1)
7.4 Adaption of the Geometric Approach to MNA Based System of Equations
127(1)
7.4.1 Modification of the System of Equations
127(1)
7.5 Application on Two Simple Example Circuits
128(6)
7.5.1 Emitter Coupled Multivibrator
128(4)
7.5.2 Schmitt Trigger
132(2)
7.6 Conclusion
134(3)
References
135(2)
8 Dynamics of Lienard Optoelectronic Oscillators
137(22)
Bruno Romeira
Jose Figueiredo
Charles N. Ironside
Julien Javaloyes
8.1 Introduction
137(2)
8.2 Resonant Tunneling Diode Optoelectronic Oscillators
139(7)
8.2.1 Resonant Tunneling Diode
140(2)
8.2.2 RTD Photo-Detector Equivalent Electrical Circuit
142(1)
8.2.3 Laser Diode Rate Equations
143(2)
8.2.4 Forced Lienard OEO System with Time Delayed Feedback
145(1)
8.3 Dynamical Regimes of Lienard OEOs
146(9)
8.3.1 Self-Sustained Oscillations
147(1)
8.3.2 Injection Locking Dynamics
148(4)
8.3.3 Quasi-Periodicity and Chaotic Dynamics
152(1)
8.3.4 Time Delayed Feedback Dynamics
152(3)
8.4 Conclusion and Future Work
155(4)
References
156(3)
9 Application of Coupled Dynamical Systems for Communities Detection in Complex Networks
159(22)
Nikolai Nefedov
9.1 Introduction
159(2)
9.2 Community Detection
161(2)
9.2.1 Modularity Maximization
161(1)
9.2.2 Communities Detection with Random Walk
161(2)
9.3 Topology Detection Using Coupled Dynamical Systems
163(5)
9.3.1 Laplacian Formulation of Network Dynamics
163(2)
9.3.2 Dynamical Structures with Different Coupling Scenarios
165(3)
9.4 Overlapping Communities
168(3)
9.4.1 Multi-membership
168(1)
9.4.2 Application of Soft Community Detection for Recommendation Systems
169(2)
9.5 Methods Testing in Benchmark Networks
171(5)
9.5.1 Zachary Karate Club: Communities and Its Dynamics
171(1)
9.5.2 Comparison of Different Predictions Schemes
172(3)
9.5.3 Detection of Negative Relations
175(1)
9.6 Applications for Mobile Networks Data
176(2)
9.7 Conclusions
178(3)
References
179(2)
10 Infinite Networks of Hubs, Spirals, and Zig-Zag Patterns in Self-sustained Oscillations of a Tunnel Diode and of an Erbium-doped Fiber-ring Laser
181(18)
Ricardo E. Francke
Thorsten Poschel
Jason A.C. Gallas
10.1 Introduction
181(2)
10.2 The Flow Defined by a Simple Circuit with a Tunnel Diode
183(2)
10.3 The Slow-Fast Dynamics of the Circuit with a Tunnel Diode
185(2)
10.4 Phase Diagrams
187(6)
10.5 Conclusions and Outlook
193(6)
References
195(1)
Appendix: The erbium-doped dual-ring fiber laser
196(3)
11 Study of Dynamics of Atmospheric Pollution and Its Association with Environmental Parameters
199(12)
Siwek Krzysztof
Osowski Stanislaw
Swiderski Bartosz
11.1 Introduction
199(1)
11.2 Analysis of the Pollution Time Series
200(5)
11.3 The Relations between the Pollution and the Environmental Parameters
205(2)
11.4 Comparison of the Linear and Nonlinear Prediction Models
207(3)
11.5 Conclusions
210(1)
References
210(1)
12 System Dynamics Modeling of Intelligent Transportation Systems Human and Social Requirements for the Construction of Dynamic Hypotheses
211(16)
Oana Mitrea
12.1 Introduction
211(1)
12.2 Interaction and Interactivity in Intelligent Transportation Systems
212(5)
12.3 Particularization: Human and Social Requirements for the System Dynamics Modeling of Cooperative Traffic Scenarios
217(5)
12.3.1 Description of the Pro-active and Co-operative Agency [ 24]
220(1)
12.3.2 The Level of Interpersonal Interaction, Intra-activity (Interaction among Technical Agents) and Interactivity with Human and Social Systems [ 24]
220(1)
12.3.3 The "Hybrid Constellations" of Pro-active and Cooperative Agency [ 24]
221(1)
12.4 Implications for the Modeling of the User Acceptance
222(1)
12.5 Conclusion
223(4)
References
223(4)
13 How to Handle Societal Complexity
227(20)
Dorien DeTombe
13.1 Introduction
227(2)
13.2 How Complex Societal Problems Should Be Handled: The Compram Methodology
229(3)
13.3 Complex Societal Problems: Problem-Handling Phase 1.1: Awareness
232(1)
13.4 Complex Societal Problems: Problem-Handling Phase 1.2: Mental Idea
233(1)
13.5 Complex Societal Problems: Problem-Handling Phase 1.3: Political Agenda
234(1)
13.6 Handling a Complex Societal Problem
234(1)
13.7 Policymakers: Jump to Conclusions
235(1)
13.8 Complex Societal Problems: Uncertainty
236(1)
13.9 Are Policymakers Educated for Their Task?
236(1)
13.10 Teaching Methods and Teaching Subject
237(1)
13.11 Creative Problem Solving
237(1)
13.12 Knowledge Institutes
238(2)
13.13 Discussion: Handling Complex Societal Problems to Provide Benefits for All?
240(1)
13.14 Summary
240(7)
Part III Electromagnetics Theory, Modeling and Simulation of Real Physical Electromagnetic Prototypes
14 Electromagnetics, Systems Theory, Fluid Dynamics, and Some Fundamentals in Physics
247(26)
Alfred Fettweis
14.1 Introduction
247(2)
14.2 Electromagentic Field in Vacuum: Maxwell's Equations and Related Results
249(2)
14.3 Fluid Dynamics
251(1)
14.4 Field Velocity, Rest Field, and Energy Velocity
252(2)
14.5 The Flow Equations
254(5)
14.5.1 General Form of the Flow Equations
254(1)
14.5.2 Flow Equations of a Basal Electromagnetic Field
255(2)
14.5.3 Field Rotating around an Axis
257(2)
14.6 A Photon Model
259(2)
14.7 Towards a Model of an Electron
261(3)
14.7.1 Purely Electromagnetic Approach
261(1)
14.7.2 Incompleteness of the Original Formulation
262(2)
14.8 Travelling Particles
264(3)
14.8.1 Electron-Like Particle Observed in Different Reference Frames
264(2)
14.8.2 Dynamic Equations of an Electron-Like Model
266(1)
14.9 Quantum Mechanics
267(3)
14.9.1 Problems with the Conventional Approach
267(1)
14.9.2 Schrodinger Equation
268(2)
14.10 Conclusion
270(3)
References
271(2)
15 Fundamentals of Electrodynamics Essential Overview of EM Theory
273(20)
Branko Miskovic
15.1 Introduction
273(1)
15.2 Basic Concepts
274(1)
15.3 Static & Kinetic Interactions
275(2)
15.4 Dynamic Interaction
277(3)
15.5 Central Distributions
280(1)
15.6 Algebraic Relations
281(1)
15.7 Field Transformations
282(1)
15.8 Kinetic Law
282(1)
15.9 Differential Equations
283(2)
15.10 EM Induction
285(2)
15.11 EM Antinomies
287(2)
15.12 Structural Models
289(2)
15.13 Conclusion
291(2)
References
292(1)
16 Advanced Adaptive Algorithms in 2D Finite Element Method of Higher Order of Accuracy
293(18)
Pavel Karban
Ivo Dolezel
Frantisek Mach
Bohus Ulrych
16.1 Introduction
293(1)
16.2 Adaptivity Techniques in Agros and Hermes
294(2)
16.3 Error of Solution
296(1)
16.4 Illustrative Examples
297(11)
16.4.1 Example I (hp Adaptivity)
298(2)
16.4.2 Example II (Curved Elements)
300(2)
16.4.3 Example III (Curved Elements and Circular Points)
302(6)
16.5 Conclusion
308(3)
References
309(2)
17 SPICE Model for Fast Time Domain Simulation of Power Transformers, Exploiting the Ferromagnetic Hysteresis and Eddy-Currents
311(14)
Lucian Mandache
Dumitru Topan
Mihai Iordache
Ioana Gabriela Sirbu
17.1 Introduction
311(2)
17.2 Modeling Principles
313(3)
17.3 SPICE Implementation
316(2)
17.4 Example of Modeling and Simulation of a Single-Phase Power Transformer
318(5)
17.5 Conclusion
323(2)
References
324(1)
18 Hard-Coupled Modeling of Induction Shrink Fit of Gas-Turbine Active Wheel
325(18)
Vaclav Kotlan
Pavel Karban
Bonus Ulrych
Ivo Dolezel
Pavel Kus
18.1 Introduction
325(2)
18.2 Formulation of the Problem and Its Basic Analysis
327(3)
18.3 Continuous Mathematical Model of the Process of Heating
330(1)
18.4 Numerical Solution
331(1)
18.5 Illustrative Example
332(6)
18.6 Conclusion
338(5)
References
338(5)
Part IV Theory of Stability and Recent Trends
19 Stability Analysis and Limit Cycles of High Order Sigma-Delta Modulators
343(24)
Valeri Mladenov
19.1 Introduction
343(1)
19.2 Parallel Decomposition of a Sigma Delta Modulator
344(4)
19.3 Stability of Shifted First Order Sigma-Delta Modulators
348(2)
19.4 Stability of High Order Sigma-Delta Modulators
350(5)
19.5 Analysis of Limit Cycles in High Order Sigma-Delta Modulators
355(9)
19.6 Conclusions
364(3)
References
364(3)
20 Stability Analysis of Vector Equalization Based on Recurrent Neural Networks
367(22)
Mohamad Mostafa
Werner G. Teich
Jurgen Lindner
20.1 Organization of the
Chapter
367(1)
20.2 Vector-Valued Transmission Model
368(2)
20.3 Recurrent Neural Networks
370(3)
20.3.1 Discrete-Time RNNs
370(1)
20.3.2 Continuous-Time RNNs
371(1)
20.3.3 Stability Analysis Based on Lyapunov Functions
371(2)
20.4 Stability Analysis of RNNs with Time-Invariant Activation Functions
373(2)
20.5 Analyzing The Optimum Activation Function
375(4)
20.5.1 The Optimum Activation Function
375(1)
20.5.2 Properties of the Optimum Activation Function
376(2)
20.5.3 Lyapunov Function vs. Maximum Likelihood Function
378(1)
20.6 Stability Analysis of RNNs with Time-Variant Activation Functions
379(3)
20.6.1 Discrete-Time RNNs with Parallel Update
379(1)
20.6.2 Discrete-Time RNN with Serial Update
380(2)
20.6.3 Continuous-Time RNN
382(1)
20.7 Global vs. Local Stability for Vector Equalizer Based on RNN
382(3)
20.7.1 Discrete-Time RNN with Parallel Update
383(1)
20.7.2 Continuous-Time RNN
383(1)
20.7.3 Discussion
383(2)
20.8 Conclusion
385(4)
References
385(4)
21 Speeding Up Linear Consensus in Networks
389(18)
Leonidas Georgopoulos
Alireza Khadivi
Martin Hasler
21.1 Introduction
389(1)
21.2 Potential Application: Forest Fire Localization
390(4)
21.3 Potential Application: Distributed Machine Learning
394(1)
21.4 Basic Linear Distributed Average Consensus Algorithm
395(2)
21.5 Optimizing the Weight Matrix for High Asymptotic Convergence Rate
397(2)
21.6 Optimizing the Convergence Rate at Finite Time
399(2)
21.7 Exact Linear Consensus at Finite Time
401(3)
21.8 Conclusions
404(3)
22 Stability of Linear Circuits with Interval Data: A Case Study
407(10)
Zygmunt A. Garczarczyk
22.1 Introduction
407(1)
22.2 Problem Statement
408(1)
22.3 Stability Of Interval Matrices
409(2)
22.4 Computational Aspects
411(1)
22.5 Numerical Experiments
412(1)
22.6 Final Remarks
413(4)
References
413(4)
Part V Further Application Area - Optimization, Data Mining, Pattern Recognition and Image Processing
23 Data Reconciliation and Bias Estimation in On-Line Optimization
417(12)
Moufid Mansour
23.1 Introduction
417(1)
23.2 Data Reconciliation
418(4)
23.2.1 Types of Errors
418(1)
23.2.2 Brief History
419(1)
23.2.3 The Benefits of Data Reconciliation
420(1)
23.2.4 Recent Developments and Software Packages
420(1)
23.2.5 Formulation of the Data Reconciliation Problem
421(1)
23.3 Bias Estimation
422(1)
23.4 ISOPE and the Inclusion of Data Reconciliation and Bias Estimation
423(1)
23.5 Application to a Continuous Stirred Tank Reactor System
424(3)
23.6 Conclusion
427(2)
References
427(2)
24 Image Edge Detection and Orientation Selection with Coupled Nonlinear Excitable Elements
429(20)
Atsushi Nomura
Yoshiki Mizukami
Koichi Okada
Makoto Ichikawa
24.1 Introduction
429(2)
24.2 Background
431(2)
24.2.1 Coupled Nonlinear Elements
431(1)
24.2.2 Edge Detection
432(1)
24.3 FitzHugh-Nagumo Elements on a Grid System
433(3)
24.3.1 FitzHugh-Nagumo Element
433(2)
24.3.2 Coupled Elements
435(1)
24.4 Algorithm
436(4)
24.4.1 Edge Detection Algorithm with a Two-Dimensional Grid System
437(1)
24.4.2 Algorithm for Edge Detection and Orientation Selection
438(2)
24.5 Experimental Results and Discussion
440(6)
24.5.1 Examples of Edge Detection and Orientation Selection
440(3)
24.5.2 Quantitative Performance Evaluation on Edge Detection
443(3)
24.6 Conclusion
446(3)
References
447(2)
25 Consecutive Repeating State Cycles Determine Periodic Points in a Turing Machine
449(19)
Michael Stephen Fiske
25.1 Introduction
449(2)
25.2 Turing Machines & Periodic Configurations
451(3)
25.3 State Cycles
454(3)
25.4 Prime Directed Edge Sequences
457(4)
25.5 Search Procedure for Periodic Points
461(6)
25.6 Discussion and Further Work
467(1)
References 468(1)
Appendix 468(7)
Author Index 475
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