Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A In 2 Volumes Volume Ii
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Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A In 2 Volumes Volume Ii
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Author : Leon O Chua
language : en
Publisher: World Scientific
Release Date : 2007-07-10
Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A In 2 Volumes Volume Ii written by Leon O Chua and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-10 with Science categories.
This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram's monumental ';New Kind of Science.';
Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A In 2 Volumes Volume I
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Author : Leon O Chua
language : en
Publisher: World Scientific
Release Date : 2006-06-08
Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A In 2 Volumes Volume I written by Leon O Chua and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-08 with Science categories.
This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram's monumental ';New Kind of Science.';
Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A Volume Iii
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Author : Leon O Chua
language : en
Publisher: World Scientific
Release Date : 2009-08-11
Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A Volume Iii written by Leon O Chua and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-11 with Computers categories.
Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli στ-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. Explicit global state transition formulas derived for rules 60, 90, 105, and 150 reveal a new scale-free phenomenon. The most surprising new result unveiled in this volume is the “Isle of Eden” found hidden in most (almost 90%) of the 256 local rules. Readers are challenged to hunt for long-period, isolated Isles of Eden. These are rare gems waiting to be discovered.
Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A Volume Vi
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Author : Leon O Chua
language : en
Publisher: World Scientific
Release Date : 2013-07-10
Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science A Volume Vi written by Leon O Chua and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-10 with Mathematics categories.
This invaluable volume ends the quest to uncover the secret recipes for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor (i.e. after the transients had disappeared) is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables. As befitting the contents aimed at school children, it was found pedagogically appealing to code each truth table by coloring each of the 8 vertices of a cubical graph in red (for binary state 1), or blue (for binary state 0), forming a toy universe of 256 Boolean cubes, each bearing a different vertex color combination.The corresponding collection of 256 distinct Boolean cubes are then segegrated logically into 6 distinct groups where members from each group share certain common dynamics which allow the long-term evolution of the color configuration of each bit string, of arbitrary length, to be predicted painlessly, via a toy-like gaming procedure, without involving any calculation. In particular, the evolution of any bit string bearing any initial color configuration which resides in any one of the possibly many distinct attractors, can be systematically predicted, by school children who are yet to learn arithmetic, via a simple recipe, for any Boolean cube belonging to group 1, 2, 3, or 4. The simple recipe for predicting the time-asymptotic behaviors of Boolean cubes belonging to groups 1, 2, and 3 has been covered in Vols. I, II, ..., V.This final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the Bernoulli rules, belonging to group 4. Here, for almost half of the toy universe, surprisingly simple recipes involving only the following three pieces of information are derived in Vol. VI; namely, a positive integer τ, a positive, or negative, integer σ, and a sign parameter β > 0, or β 0. In particular, given any color configuration belonging to an attractor of any one of the 108 Boolean cubes from group 4, any child can predict the color configuration after τ generations, without any computation, by merely shifting each cell σ bits to the left (resp. right) if σ 0 (resp. σ
Chaos Cnn Memristors And Beyond A Festschrift For Leon Chua With Dvd Rom Composed By Eleonora Bilotta
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Author : Andrew Adamatzky
language : en
Publisher: World Scientific
Release Date : 2013-01-02
Chaos Cnn Memristors And Beyond A Festschrift For Leon Chua With Dvd Rom Composed By Eleonora Bilotta written by Andrew Adamatzky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-02 with Mathematics categories.
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.
A Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science
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Author : Leon O. Chua
language : en
Publisher: World Scientific
Release Date : 2013
A Nonlinear Dynamics Perspective Of Wolfram S New Kind Of Science written by Leon O. Chua and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
This text uncovers secret recipes from the abstract theory of one-dimensional cellular automata for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables.
2 D Quadratic Maps And 3 D Ode Systems A Rigorous Approach
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Author : Zeraoulia Elhadj
language : en
Publisher: World Scientific
Release Date : 2010-07-08
2 D Quadratic Maps And 3 D Ode Systems A Rigorous Approach written by Zeraoulia Elhadj and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-08 with Science categories.
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.
Wave Momentum And Quasi Particles In Physical Acoustics
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Author : Gerard A Maugin
language : en
Publisher: World Scientific
Release Date : 2015-03-26
Wave Momentum And Quasi Particles In Physical Acoustics written by Gerard A Maugin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-26 with Science categories.
This unique volume presents an original approach to physical acoustics with additional emphasis on the most useful surface acoustic waves on solids. The study is based on foundational work of Léon Brillouin, and application of the celebrated invariance theorem of Emmy Noether to an element of volume that is representative of the wave motion.This approach provides an easy interpretation of typical wave motions of physical acoustics in bulk, at surfaces, and across interfaces, in the form of the motion of associated quasi-particles. This type of motion, Newtonian or not, depends on the wave motion considered, and on the original modeling of the continuum that supports it. After a thoughtful review of Brillouin's fundamental ideas related to radiative stresses, wave momentum and action, and the necessary reminder on modern nonlinear continuum thermomechanics, invariance theory and techniques of asymptotics, a variety of situations and models illustrates the power and richness of the approach and its strong potential in applications. Elasticity, piezoelectricity and new models of continua with nonlinearity, viscosity and some generalized features (microstructure, weak or strong nonlocality) or unusual situations (bounding surface with energy, elastic thin film glued on a surface waveguide), are considered, exhibiting thus the versatility of the approach.This original book offers an innovative vision and treatment of the problems of wave propagation in deformable solids. It opens up new horizons in the theoretical and applied facets of physical acoustics.
Integral Dynamical Models Singularities Signals And Control
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Author : Denis Sidorov
language : en
Publisher: World Scientific
Release Date : 2014-09-05
Integral Dynamical Models Singularities Signals And Control written by Denis Sidorov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-05 with Science categories.
This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis.
Topology And Dynamics Of Chaos
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Author : Christophe Letellier
language : en
Publisher: World Scientific
Release Date : 2013
Topology And Dynamics Of Chaos written by Christophe Letellier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.
The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,