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This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.
Elegant Circuits: Simple Chaotic Oscillators by Julien Clinton Sprott,Wesley Joo-chen Thio Pdf
Chaos is the study of the underlying determinism in the seemingly random phenomena that occur all around us. One of the best experimental demonstrations of chaos occurs in electrical circuits when the parameters are chosen carefully. We will show you how to construct such chaotic circuits for use in your own studies and demonstrations while teaching you the basics of chaos.This book should be of interest to researchers and hobbyists looking for a simple way to produce a chaotic signal. It should also be useful to students and their instructors as an engaging way to learn about chaotic dynamics and electronic circuits. The book assumes only an elementary knowledge of calculus and the ability to understand a schematic diagram and the components that it contains.You will get the most out of this book if you can construct the circuits for yourself. There is no substitute for the thrill and insight of seeing the output of a circuit you built unfold as the trajectory wanders in real time across your oscilloscope screen. A goal of this book is to inspire and delight as well as to teach.
Chaos in Nonlinear Oscillators by Muthusamy Lakshmanan,K. Murali Pdf
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
Sinusoidal Oscillators and Waveform Generators using Modern Electronic Circuit Building Blocks by Raj Senani,D. R. Bhaskar,V. K. Singh,R. K. Sharma Pdf
This book serves as a single-source reference to sinusoidal oscillators and waveform generators, using classical as well as a variety of modern electronic circuit building blocks. It provides a state-of-the-art review of a large variety of sinusoidal oscillators and waveform generators and includes a catalogue of over 600 configurations of oscillators and waveform generators, describing their relevant design details and salient performance features/limitations. The authors discuss a number of interesting, open research problems and include a comprehensive collection of over 1500 references on oscillators and non-sinusoidal waveform generators/relaxation oscillators. Offers readers a single-source reference to everything connected to sinusoidal oscillators and waveform generators, using classical as well as modern electronic circuit building blocks; Provides a state-of-the-art review of a large variety of sinusoidal oscillators and waveform generators; Includes a catalog of over 600 configurations of oscillators and waveform generators, with their relevant design details and their salient performance features/limitations.
Topics on Chaotic Systems by Charilaos Skiadas,Ioannis Dimotikalis Pdf
This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences. It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications. These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.
Chaos in Circuits and Systems by Guanrong Chen,Tetsushi Ueta Pdf
In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.
Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization by Esteban Tlelo-Cuautle,Luis Gerardo de la Fraga,Omar Guillén-Fernández,Alejandro Silva-Juárez Pdf
Mathematicians have devised different chaotic systems that are modeled by integer or fractional-order differential equations, and whose mathematical models can generate chaos or hyperchaos. The numerical methods to simulate those integer and fractional-order chaotic systems are quite different and their exactness is responsible in the evaluation of characteristics like Lyapunov exponents, Kaplan-Yorke dimension, and entropy. One challenge is estimating the step-size to run a numerical method. It can be done analyzing the eigenvalues of self-excited attractors, while for hidden attractors it is difficult to evaluate the equilibrium points that are required to formulate the Jacobian matrices. Time simulation of fractional-order chaotic oscillators also requires estimating a memory length to achieve exact results, and it is associated to memories in hardware design. In this manner, simulating chaotic/hyperchaotic oscillators of integer/fractional-order and with self-excited/hidden attractors is quite important to evaluate their Lyapunov exponents, Kaplan-Yorke dimension and entropy. Further, to improve the dynamics of the oscillators, their main characteristics can be optimized applying metaheuristics, which basically consists of varying the values of the coefficients of a mathematical model. The optimized models can then be implemented using commercially available amplifiers, field-programmable analog arrays (FPAA), field-programmable gate arrays (FPGA), microcontrollers, graphic processing units, and even using nanometer technology of integrated circuits. The book describes the application of different numerical methods to simulate integer/fractional-order chaotic systems. These methods are used within optimization loops to maximize positive Lyapunov exponents, Kaplan-Yorke dimension, and entropy. Single and multi-objective optimization approaches applying metaheuristics are described, as well as their tuning techniques to generate feasible solutions that are suitable for electronic implementation. The book details several applications of chaotic oscillators such as in random bit/number generators, cryptography, secure communications, robotics, and Internet of Things.
Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption by Banerjee, Santo Pdf
Over the past few decades, there has been numerous research studies conducted involving the synchronization of dynamical systems with several theoretical studies and laboratory experimentations demonstrating the pivotal role for this phenomenon in secure communications. Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption explores the combination of ordinary and time delayed systems and their applications in cryptographic encoding. This innovative publication presents a critical mass of the most sought after research, providing relevant theoretical frameworks and the latest empirical research findings in this area of study.
Advances and Applications in Chaotic Systems by Sundarapandian Vaidyanathan,Christos Volos Pdf
This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.
Proceedings of the 2nd Experimental Chaos Conference by W Ditto,L Pecora,S Vohra,M Shlesinger,M Spano Pdf
The 2nd experimental chaos conference provided a multidisciplinary forum for the scientific and engineering communities to present recent developments of and techniques in nonlinear dynamics. Major themes included control, synchronization, signal detection/characterization and communication. Major fields of interest included lasers, fluids, magnetics, electronics, chemically reacting fluids, cardiology, neurobiology and environmental sciences. Contents:Experimental Studies of Chaotic Mixing (J M Ottino et al)Using Random Maps in the Analysis of Experimental Fluid Flows (J C Sommerer)Chaos, Patterns and Defects in Stimulated Scattering Phenomena (R G Harrison)Test of the Normal Form for a Subcritical Bifurcation (K Wiesenfeld et al)Controlling Symbolic Dynamics for Communication (S Hayes et al)Control of Chaos in a CO2 Laser (J M Perez et al)Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure (M A Davies & F C Moon)Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source (R G Holt et al)Quantum Chaos Experiments Using Microwave Cavities (A Kudrolli & S Sridhar)When Small Noise Imposed on Deterministic Dynamics Becomes Important (M Franaszek & L Fronzoni)Chaos Control for Cardiac Arrhythmias (J N Weiss et al)Broad-Band Synchronization in Monkey Neocortex (S L Bressler et al)Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats (Y Almog et al)Tests for Deterministic Chaos in Noisy Time Series (T Chang et al)The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance (E Pantazelou et al)Chaos During Heterogeneous Chemical Reactions (J L Hudson)Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems (V Petrov et al)Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System (P Parmananda et al)Temperature Patterns on Catalytic Surfaces (D Luss)and other papers Readership: Physicists, mathematicians, engineers, biologists and chemists.keywords:
Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives by Mark Edelman,Elbert E. N. Macau,Miguel A. F. Sanjuan Pdf
The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.
Phase Resetting in Medicine and Biology by Peter A. Tass Pdf
This book presents a new theoretical approach to phase resetting and stimulation-induced synchronization and desynchronization in a population of oscillators. The author uses stochastic methods from statistical mechanics and applies his theory to models of practical importance in physiology and neuroscience. The book is accessible to readers not familiar with the mathematical formalism. The author also proposes improvements to stimulation techniques as used by neurologists and neurosurgeons in the context of Parkinson's disease and MEG/EEG data analysis.
Handbook of Chaos Control by Eckehard Schöll,Heinz Georg Schuster Pdf
This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community. An interdisciplinary approach of interest to scientists and engineers working in a number of areas.
Chaos, CNN, Memristors and Beyond by Andrew Adamatzky,Guanrong Chen Pdf
This invaluable book is a unique collection of tributes to outstanding discoveries pioneered by Leon Chua in nonlinear circuits, cellular neural networks, and chaos. It is comprised of three parts. The first — cellular nonlinear networks, nonlinear circuits and cellular automata — deals with Chua's Lagrangian circuits, cellular wave computers, bio-inspired robotics and neuro-morphic architectures, toroidal chaos, synaptic cellular automata, history of Chua's circuits, cardiac arrhythmias, local activity principle, symmetry breaking and complexity, bifurcation trees, and Chua's views on nonlinear dynamics of cellular automata. Dynamical systems and chaos is the scope of the second part of the book, where we find genius accounts on theory and application of Julia set, stability of dynamical networks, chaotic neural networks and neocortical dynamics, dynamics of piecewise linear systems, chaotic mathematical circuitry, synchronization of oscillators, models of catastrophic events, control of chaotic systems, symbolic dynamics, and solitons. First hand accounts on the discovery of memristors in HP Labs, historical excursions into ‘ancient memristors’, analytical analysis of memristors, and hardware memristor emulators are presented in the third and final part of the book. The book is quintessence of ideas on future and emergent hardware, analytic theories of complex dynamical systems and interdisciplinary physics. It is a true Renaissance volume where bright ideas of electronics, mathematics and physics enlighten facets of modern science. The unique DVD covers the artistic aspects of chaos, such as several stunningly melodious musical compositions using chaotic atttractors, a virtual gallery of hundreds of colorful attractors, and even a cartoon-like play on the genesis of Chua's circuit that was based on a widely acclaimed performance in Rome and other venues in Italy. In short, it is a veritable kaleiscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike. Contents:Cellular Nonlinear Networks, Nonlinear Circuits and Cellular Automata:Genealogy of Chua's Circuit (Peter Kennedy)Impasse Points, Mutators, and Other Chua Creations (Hyongsuk Kim)Chua's Lagrangian Circuit Elements (Orla Feely)From CNN Dynamics to Cellular Wave Computers (Tamas Roska)Contributions of CNN to Bio-Robotics and Brain Science (Paolo Arena and Luca Patané)From Radio-amateurs' Electronics to Toroidal Chaos (Otto E Rössler and Christophe Letellier)Analyzing the Dynamics of Excitatory Neural Networks by Synaptic Cellular Automata (V Nekorkin, A Dmitrichev, D Kasatkin and V Afraimovich)Dynamical Systems Perspective of Wolfram's Cellular Automata (M Courbage and B Kamińki)The Genesis of Chua's Circuit: Connecting Science, Art and Creativity (Francesca Bertacchini, Eleonora Bilotta, Giuseppe Laria and Pietro Pantano)Nonlinear Electronics Laboratory (NOEL): A Reminiscence (Chai Wah Wu)Bursting in Cellular Automata and Cardiac Arrhythmias (Gil Bub, Alvin Shrier and Leon Glass)Local Activity Principle: The Cause of Complexity and Symmetry Breaking (Klaus Mainzer)Explorations in the Forest of Bifurcation Trees: Route from Chua's Circuit to Chua's Memristive Oscillator (Łukasz Czerwiński and Maciej J Ogorzałek)Chua's Nonlinear Dynamics Perspective Cellular Automata (Giovanni E Pazienza)Application of CNN to Brainlike Computing (Bertram E Shi)Ideal Turbulence Phenomenon and Transmission Line with Chua's Diode (E Yu Romanenko and A N Sharkovsky)Chaos in Electronic Circuits: Chua's Contribution (1980–2000) (Christophe Letellier)Dynamical Systems and Chaos:Connectivity of Julia Sets for Singularly Perturbed Rational Maps (Robert L Devaney and Elizabeth D Russell)Structural Transformations and Stability of Dynamical Networks (L A Bunimovich and B Z Webb)Chua's Time (Arturo Buscarino, Luigi Fortuna and Mattia Frasca)Chaotic Neural Networks and Beyond (Kazuyuki Aihara, Taiji Yamada and Makito Oku)Chaotic Neocritical Dynamics (Walter J Freeman)Nonlinear Dynamics of a Class of Piecewise Linear Systems (M Lakshmanan and K Murali)Chaotic Mathematical Circuitry (R Lozi)Chua's Equation was Proved to be Chaotic in Two Years, Lorenz Equation in Thirty Six Years (Bharathwaj Muthuswamy)Toward a Quantitative Formulation of Emergence (G Nicolis)Controlled Synchronization of Chaotic Oscillators with Huygens' Coupling (J Peńa-Ramírez, R H B Fey and H Nijmeijer)Using Time-Delay Feedback for Control and Synchronization of Dynamical Systems (Kestutis Pyragas, Viktoras Pyragas and Tatjana Pyragiene)Models of Catastrophic Events and Suggestions to Foretell Them (Yves Pomeau and Martine Le Berre)Synchronization Propensity in Networks of Dynamical Systems: A Purely Topological Indicator (Stefano Fasani and Sergio Rinaldi)Further Progress in Partial Control of Chaotic Systems (Juan Sabuco, Miguel Sanjuan and Samuel Zambrano)Phase and Complete Synchronizations in Time-Delay Systems (D V Senthilkumar, M Manju Shrii and J Kurths)Symbolic Dynamics and Spiral Structures due to the Saddle-Focus Bifurcations (Andrey Shilnikov, Leonid Shilnikov and Roberto Barrio)Dynamics of Periodically Forced Mass Point on Constrained Surface with Changing Curvature (Yoshisuke Ueda)Solitons for Describing 3-D Physical Reality: The Current Frontier (Paul J Werbos)Thermal Solitons in 1D and 2D Anharmonic Lattices — Solectrons and the Organization of Non-Linear Fluctuations in Long-Living Dynamical Structures (M G Velarde, W Ebeling and A P Chetverikov)Global Optimizations by Intermittent Diffusion (Shui-Nee Chow, Tzi-Sheng Yang and Hao-Min Zhou)Memristors:How We Found the Missing Memristor (R Stanley Williams)Aftermath of Finding the Memristor (R Stanley Williams)The Singing Arc: The Oldest Memristor? (Jean-Marc Ginoux and Bruno Rossetto)Two Centuries of Memristors (Themistoklis Prodromakis)State Equations for Active Circuits with Memristors (Martin Hasler)Analytical Analysis of Memristive Networks (Torsten Schmidt, Willi Neudeck, Ute Feldmann and Ronald Tetzlaff)Hardware Memristor Emulators (Andrew L Fitch, Herbert H C Iu and Chi K Tse)Leon Chua's Memristor (Guanrong Chen) Readership: Graduate students, researchers and academics in all engineering disciplines as well as historians of science. Keywords:Memristors;CNN;Chaos;Dynamical SystemsKey Features:Unique personality of Leon Chua and enormity of his achievements underpins the structure of the bookConglomerate of hot topics: memristors, chaos, computationalOriginal papers from renown scholars and researchers as well as numerous tutorials and historical expositions on each of the topicsHigh pedagogical value makes the book a timeless referenceReviews: "It is a veritable kaleidoscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike." Zentralblatt MATH
