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Determining Thresholds Of Complete Synchronization And Application
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Book Synopsis Determining Thresholds Of Complete Synchronization, And Application by : Andrzej Stefanski
Download or read book Determining Thresholds Of Complete Synchronization, And Application written by Andrzej Stefanski and published by World Scientific. This book was released on 2009-06-05 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology, communication or laser physics. Over the last decade, new types of synchronization have been identified and some interesting new ideas concerning the synchronization have also appeared.This book presents the complete synchronization problem rather than just results from the research. The problem is demonstrated in relation to a kind of coupling applied between dynamical systems, whereby a unique classification of possible couplings is introduced. Another novel feature is the connection presented between synchronization and the problem of determining the Lyapunov exponents, especially for non-differentiable systems. A detailed proposal of such an estimation method and examples of its application are included.
Book Synopsis Determining Thresholds of Complete Synchronization, and Application by : Andrzej Stefanski
Download or read book Determining Thresholds of Complete Synchronization, and Application written by Andrzej Stefanski and published by World Scientific. This book was released on 2009 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology, communication or laser physics. Over the last decade, new types of synchronization have been identified and some interesting new ideas concerning the synchronization have also appeared. This book presents the complete synchronization problem rather than just results from the research. The problem is demonstrated in relation to a kind of coupling applied between dynamical systems, whereby a unique classification of possible couplings is introduced. Another novel feature is the connection presented between synchronization and the problem of determining the Lyapunov exponents, especially for non-differentiable systems. A detailed proposal of such an estimation method and examples of its application are included.
Book Synopsis Robust Chaos and Its Applications by : Elhadj Zeraoulia
Download or read book Robust Chaos and Its Applications written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2012 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.
Book Synopsis Fractional Order Systems: Modeling And Control Applications by : Riccardo Caponetto
Download or read book Fractional Order Systems: Modeling And Control Applications written by Riccardo Caponetto and published by World Scientific. This book was released on 2010-02-10 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to propose the implementation and application of Fractional Order Systems (FOS). It is well known that FOS can be utilized in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductory chapters are included on the definition of stability region of Fractional Order PID Controller and Chaotic FOS, followed by the practical implementation based on Microcontroller, Field Programmable Gate Array, Field Programmable Analog Array and Switched Capacitor. Another section is dedicated to FO modeling of Ionic Polymeric Metal Composite (IPMC). This new material will have applications in robotics, aerospace and biomedicine.
Book Synopsis Chaos in Nature by : Christophe Letellier
Download or read book Chaos in Nature written by Christophe Letellier and published by World Scientific. This book was released on 2013 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos theory deals with the description of motion (in a general sense) which cannot be predicted in the long term although produced by deterministic system, as well exemplified by meteorological phenomena. It directly comes from the Lunar theory OCo a three-body problem OCo and the difficulty encountered by astronomers to accurately predict the long-term evolution of the Moon using OC NewtonianOCO mechanics. Henri Poincar(r)''s deep intuitions were at the origin of chaos theory. They also led the meteorologist Edward Lorenz to draw the first chaotic attractor ever published. But the main idea consists of plotting a curve representative of the system evolution rather than finding an analytical solution as commonly done in classical mechanics. Such a novel approach allows the description of population interactions and the solar activity as well. Using the original sources, the book draws on the history of the concepts underlying chaos theory from the 17th century to the last decade, and by various examples, show how general is this theory in a wide range of applications: meteorology, chemistry, populations, astrophysics, biomedicine, et
Book Synopsis Development of Memristor Based Circuits by : Herbert Ho-Ching Iu
Download or read book Development of Memristor Based Circuits written by Herbert Ho-Ching Iu and published by World Scientific. This book was released on 2013 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summary: "As memristors are not yet on the market, the development of memristor emulators and memristor based circuits is very important for real and practical engineering applications. The objectives of this book are to review the basic concepts of the memristor, describe state-of-the-art memristor based circuits and to stimulate further research and development in this area."--Preface.
Book Synopsis Modeling by Nonlinear Differential Equations by : Paul E. Phillipson
Download or read book Modeling by Nonlinear Differential Equations written by Paul E. Phillipson and published by World Scientific. This book was released on 2009 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions."--back cover.
Book Synopsis Mathematical Mechanics by : Ellis D. Cooper
Download or read book Mathematical Mechanics written by Ellis D. Cooper and published by World Scientific. This book was released on 2011 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unprecedented book offers all the details of the mathematical mechanics underlying state-of-the-art modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding. The method is to take advantage of modern mathematical technology — Eilenberg-Mac Lane category theory, Robinson infinitesimal calculus and Kolmogorov probability theory — to examine a succession of distinguishable universes of particles, and continuous, thermodynamic, chemical, and molecular bodies, all with a focus on proofs by algebraic calculation without set theory. Also provided are metaphors and analogies, and careful distinction between representational pictures, mental model drawings, and mathematical diagrams.High school mathematics teachers, undergraduate and graduate college students, and researchers in mathematics, physics, chemistry, and biology may use this integrated publication to broaden their perspective on science, and to experience the precision that mathematical mechanics brings to understanding the muscular mechanism of nearly all animal behavior.
Book Synopsis Bifurcations in Piecewise-smooth Continuous Systems by : David John Warwick Simpson
Download or read book Bifurcations in Piecewise-smooth Continuous Systems written by David John Warwick Simpson and published by World Scientific. This book was released on 2010 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Fundamentals of piecewise-smooth, continuous systems. 1.1. Applications. 1.2. A framework for local behavior. 1.3. Existence of equilibria and fixed points. 1.4. The observer canonical form. 1.5. Discontinuous bifurcations. 1.6. Border-collision bifurcations. 1.7. Poincaré maps and discontinuity maps. 1.8. Period adding. 1.9. Smooth approximations -- 2. Discontinuous bifurcations in planar systems. 2.1. Periodic orbits. 2.2. The focus-focus case in detail. 2.3. Summary and classification -- 3. Codimension-two, discontinuous bifurcations. 3.1. A nonsmooth, saddle-node bifurcation. 3.2. A nonsmooth, Hopf bifurcation. 3.3. A codimension-two, discontinuous Hopf bifurcation -- 4. The growth of Saccharomyces cerevisiae. 4.1. Mathematical model. 4.2. Basic mathematical observations. 4.3. Bifurcation structure. 4.4. Simple and complicated stable oscillations -- 5. Codimension-two, border-collision bifurcations. 5.1. A nonsmooth, saddle-node bifurcation. 5.2. A nonsmooth, period-doubling bifurcation -- 6. Periodic solutions and resonance tongues. 6.1. Symbolic dynamics. 6.2. Describing and locating periodic solutions. 6.3. Resonance tongue boundaries. 6.4. Rotational symbol sequences. 6.5. Cardinality of symbol sequences. 6.6. Shrinking points. 6.7. Unfolding shrinking points -- 7. Neimark-Sacker-like bifurcations. 7.1. A two-dimensional map. 7.2. Basic dynamics. 7.3. Limiting parameter values. 7.4. Resonance tongues. 7.5. Complex phenomena relating to resonance tongues. 7.6. More complex phenomena
Book Synopsis Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations by : Anatoliy M. Samoilenko
Download or read book Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations written by Anatoliy M. Samoilenko and published by World Scientific. This book was released on 2011 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Differential equations with random right-hand sides and impulsive effects. 1.1. An impulsive process as a solution of an impulsive system. 1.2. Dissipativity. 1.3. Stability and Lyapunov functions. 1.4. Stability of systems with permanently acting random perturbations. 1.5. Solutions periodic in the restricted sense. 1.6. Periodic solutions of systems with small perturbations. 1.7. Periodic solutions of linear impulsive systems. 1.8. Weakly nonlinear systems. 1.9. Comments and references -- 2. Invariant sets for systems with random perturbations. 2.1. Invariant sets for systems with random right-hand sides. 2.2. Invariant sets for stochastic Ito systems. 2.3. The behaviour of invariant sets under small perturbations. 2.4. A study of stability of an equilibrium via the reduction principle for systems with regular random perturbations. 2.5. Stability of an equilibrium and the reduction principle for Ito type systems. 2.6. A study of stability of the invariant set via the reduction principle. Regular perturbations. 2.7. Stability of invariant sets and the reduction principle for Ito type systems. 2.8. Comments and references -- 3. Linear and quasilinear stochastic Ito systems. 3.1. Mean square exponential dichotomy. 3.2. A study of dichotomy in terms of quadratic forms. 3.3. Linear system solutions that are mean square bounded on the semiaxis. 3.4. Quasilinear systems. 3.5. Linear system solutions that are probability bounded on the axis. A generalized notion of a solution. 3.6. Asymptotic equivalence of linear systems. 3.7. Conditions for asymptotic equivalence of nonlinear systems. 3.8. Comments and references -- 4. Extensions of Ito systems on a torus. 4.1. Stability of invariant tori. 4.2. Random invariant tori for linear extensions. 4.3. Smoothness of invariant tori. 4.4. Random invariant tori for nonlinear extensions. 4.5. An ergodic theorem for a class of stochastic systems having a toroidal manifold. 4.6. Comments and references -- 5. The averaging method for equations with random perturbations. 5.1. A substantiation of the averaging method for systems with impulsive effect. 5.2. Asymptotics of normalized deviations of averaged solutions. 5.3. Applications to the theory of nonlinear oscillations. 5.4. Averaging for systems with impulsive effects at random times. 5.5. The second theorem of M.M. Bogolyubov for systems with regular random perturbations. 5.6. Averaging for stochastic Ito systems. An asymptotically finite interval. 5.7. Averaging on the semiaxis. 5.8. The averaging method and two-sided bounded solutions of Ito systems. 5.9. Comments and references
Book Synopsis Physarum Machines by : Andrew Adamatzky
Download or read book Physarum Machines written by Andrew Adamatzky and published by World Scientific. This book was released on 2010 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Physarum machine is a programmable amorphous biological computer experimentally implemented in the vegetative state of true slime mould Physarum polycephalum. It comprises an amorphous yellowish mass with networks of protoplasmic veins, programmed by spatial configurations of attracting and repelling gradients. This book demonstrates how to create experimental Physarum machines for computational geometry and optimization, distributed manipulation and transportation, and general-purpose computation. Being very cheap to make and easy to maintain, the machine also functions on a wide range of substrates and in a broad scope of environmental conditions. As such a Physarum machine is a 'green' and environmentally friendly unconventional computer. The book is readily accessible to a nonprofessional reader, and is a priceless source of experimental tips and inventive theoretical ideas for anyone who is inspired by novel and emerging non-silicon computers and robots. An account on Physarum Machines can be viewed at http: //www.youtube.com/user/PhysarumMachines.
Book Synopsis Discrete Systems With Memory by : Ramon Alonso-sanz
Download or read book Discrete Systems With Memory written by Ramon Alonso-sanz and published by World Scientific. This book was released on 2011-03-08 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions.It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian: only the actual configuration is taken into account to generate the next one.Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced.The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects.
Book Synopsis Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Iv) by : Leon O Chua
Download or read book Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Iv) written by Leon O Chua and published by World Scientific. This book was released on 2011-04-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume IV continues the author's odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing the fractal properties of characteristic functions, as well as explicit formulas for generating colorful and pedagogically revealing isomorphic basin tree diagrams. Many new results were derived and proved by uncovering subtle symmetries endowed by various subsets of the 256 Boolean cubes. For the first time, rigorous analyses were used to identify 67, out off 256, local rules whose asymptotic behaviors consist of robust period-l orbits. The highlight of this continuing odyssey is the discovery of an isolated period-3240 Isle of Eden hidden among the dense omega-limit orbits of Wolfram's remarkable “random number generating” rule 30. This is the largest gem known to-date and readers are challenged to uncover even larger ones.
Book Synopsis 2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach by : Zeraoulia Elhadj
Download or read book 2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach written by Zeraoulia Elhadj and published by World Scientific. This book was released on 2010-07-08 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the Hénon map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters.Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two representative systems, is the study of the invertible case of the 2-D quadratic map, where previous works are oriented toward Hénon mapping. 2-D quadratic maps are then classified into 30 maps with well-known formulas. Two proofs on the regions for chaos, hyperchaos, and non-chaos in the space of the bifurcation parameters are presented using a technique based on the second-derivative test and bounds for Lyapunov exponents. Also included is the proof of chaos in the piecewise linear Chua's system using two methods, the first of which is based on the construction of Poincaré map, and the second is based on a computer-assisted proof. Finally, a rigorous analysis is provided on the bifurcational phenomena in the piecewise linear Chua's system using both an analytical 2-D mapping and a 1-D approximated Poincaré mapping in addition to other analytical methods.
Book Synopsis Human Factors Engineering and Ergonomics by : Stephen J. Guastello
Download or read book Human Factors Engineering and Ergonomics written by Stephen J. Guastello and published by CRC Press. This book was released on 2023-04-14 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook comprehensively covers the basic principles and most recent advances regarding visual displays, auditory and tactile displays and controls; psychophysics; cognitive processes; human-computer interaction, artificial intelligence and artificial life; stress and human performance; occupational accidents and prevention; human group dynamics and complex systems; and anthropometry, workspace and environmental design. The systems perspective emphasizes nonlinear dynamics for system performance changes and emergent behaviours of complex person-machine systems. This book- • Surveys principles of conventional and computer-based machine interaction. • Assesses the relative effectiveness of accident analysis and prevention strategies. • Highlights nonlinear dynamics for system performance changes. • Examines artificial intelligence and complex systems. • Investigates sources of cognitive workload and fatigue. The textbook will be a valuable resource for advanced undergraduates and graduate students in diverse fields including ergonomics, human factors, cognitive science, computer science, operations management, and psychology. The textbook brings together core principles of person-machine interaction, accident analysis and prevention strategies, risk analysis and resilience, artificial intelligence, group dynamics, and nonlinear dynamics for an enhanced understanding of complex person-machine systems.
Book Synopsis A Practical Guide for Studying Chua's Circuits by : Recai Kilic
Download or read book A Practical Guide for Studying Chua's Circuits written by Recai Kilic and published by World Scientific. This book was released on 2009-12-31 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Autonomous and nonautonomous Chua's circuits are of special significance in the study of chaotic system modeling, chaos-based science and engineering applications. Since hardware and software-based design and implementation approaches can be applied to Chua's circuits, these circuits are also excellent educative models for studying and experimenting nonlinear dynamics and chaos.This book not only presents a collection of the author's published papers on design, simulation and implementation of Chua's circuits, it also provides a systematic approach to practising chaotic dynamics.
Book Synopsis A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science by : Leon O. Chua
Download or read book A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science written by Leon O. Chua and published by World Scientific Publishing Company. This book was released on 2006 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ch. 1. Isles of Eden. 1. Recap of main results from parts I to VI. 1.1. Local rules and Boolean cubes. 1.2. Threshold of complexity. 1.3. Only 88 local rules are independent. 1.4. Robust characterization of 70 independent local rules. 2. Basin tree diagrams of ten complex Bernoulli shift rules. 2.1. Basin of attraction and basin trees. 2.2. Garden of Eden. 2.3. Isle of Eden. 2.4. Gallery of basin tree diagrams. 3. Global analysis of local rule 90. 3.1. Ru1e 90 has no Isle of Eden. 3.2. Period of Rule 90 grows with L. 3.3. Global state-transition formula for rule 90. 3.4. Periodicity constraints of rule 90. 4. Global analysis of local rules 150 and 105. 4.1. Rules 150 and 105 are composed of Isles of Eden if L is not divisible by 3. 4.2. Global state-transition formula for rules 150 and 105. 4.3. Rules 150 and 105 are globally quasi-equivalent. 5. Concluding remarks -- ch. 2. More Isles of Eden. 1. The beginning of the end. 2. Basin tree diagrams of eight hyper Bernoulli shift rules. 2.1. Highlights from rule 26. 2.2. Highlights from rule 30. 2.3. Highlights from rule 41. 2.4. Highlights from rule 45. 2.5. Highlights from rule 60. 2.6. Highlights from rule 106. 2.7. Highlights from rule 110. 2.8. Highlights from rule 154. 3. Global analysis of local rule 60. 3.1. Rule 60 has no Isles of Eden. 3.2. Period of rule 60 grows with L. 3.3. Global state-transition formula for rule 60. 3.4. Periodicity constraints of rule 60. 4. Global analysis of local rule 154 and 45. 5. Dense Isles-of-Eden property. 5.1. Notations and definitions. 5.2. Four basic lemmas. 5.3. Locating points with multiple preimages. 5.4. Constructing the Isles of Eden digraph. 5.5. The full Isles of Eden digraph. 5.6. Nondegenerate cycles and Isles of Eden. 5.7. Effect of global equivalence transformations on Isles of Eden digraphs. 5.8. Dense Isles of Eden from rule 45 and rule 154. 5.9. Dense Isles of Eden from rule 105 and rule 150. 5.10. Gallery of Isles of Eden digraphs of eight representative local rules. 6. Concluding remarks
