a collection from leon chua - world scientific

The Chua Lectures: From Memristors and Cellular Nonlinear Networks to the Edge of Chaos

(In 4 Volumes)Volume I. Memristors: New Circuit Element with Memory

Volume II. Memristors and CNN: The Right Stuff for AI and Brain-Like ComputersVolume III. Chaos: Chua’s Circuit and Complex Nonlinear Phenomena

Volume IV. Local Activity Principle: Chua’s Riddle, Turing Machine, and Universal Computing Rule 137By (author): Leon O Chua (University of California at Berkeley, USA) Chua (University of California at Berkeley, USA)

dubbed the edge of chaos, is shown via insightful examples to be the genesis of most complex phenomena, including intelligence, creativity, and deep learning. The edge of chaos is Mother Nature’s tool for overcoming the tyranny of the second law of thermodynamics by providing an escape hatch for entropy to decrease over time. Indeed, the local activity principle which is profusely illustrated in the final volume, is widely recognized as a new law of thermodynamics, and is identified as the sine qua non of all complex phe-nomena, including life itself.

322pp Dec 2020978-981-121-544-5 US$115 £100978-981-121-545-2(ebook) US$173 £150978-981-121-592-6(mbook) US$92 £80

Volume III — presents an overview of the fascinating phenomenon called chaos, while immersing the audience with the sights and sound of chaos from the Chua Circuit, in-vented in 1984 by Leon Chua, and has now become the standard textbook example of chaos exhibited by an inexpensive (less than $10) nonlinear electronic circuit, and not by computer simulations.


Volume IV — surprises the audience with a new law of nature — dubbed the local activity principle, as discovered and proved mathe-matically in 1996 by Leon Chua. In particular, a Corollary of Chua’s local activity theorem,

Volume I — covers everything that a researcher may want to know about memristors but is too afraid to ask.


Volume II — shows that memristors can be ei-ther volatile or non-volatile, and effectively proving that synapses are non-volatile memristors, while action potentials are generated by locally-active memristors.


This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in

Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discus-sion session, and an Encore of special trivia that the audience found mesmerizing.

These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as they are discovered or invented by the author himself. Unlike most technical books that suffer a notori-ously short life span as their novelties could be superseded by superior technologies. This series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.

1062pp Dec 2020978-981-121-537-7(Set) US$368 £325

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World Scientific Series on Nonlinear Science Series A - Volume 57

A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science (Volume I & II)By (author): Leon O Chua (University of California at Berkeley, USA)

“This book is a colourful presentation with fresh ideas and attractive illustrations … those study-ing non-linear sciences, electronic engineering, mathematics and logics, complexity and emergent phenomena, and possibly even chemistry and biology will certainly discover exciting concepts, analogies and research tools in this refreshing text. Anyone from freshmen to elderly academics will find parts interesting to them. The volumes are somewhat special and exciting because they possess a unique ‘Chua brand’ and show gradual development of ideas and concepts in an edu-cational and entertaining hence mathematically rigorous manner.”

Journal of Cellular Automata

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 interpre-tations 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.”

996pp Jul 20079789812566423 (Set of 2 Vol.) US$434 £360

Vol.1 396pp Jul 2007978-981-256-977-6 US$196 £163978-981-277-213-8(ebook) US$294 £245978-981-4478-68-7(mbook) US$157 £130

Vol.2 600pp Jul 2007978-981-256-976-9 US$286 £237978-981-277-889-5(ebook) US$429 £357978-981-4478-69-4(mbook) US$229 £190


A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science (Volume III)By (author): Leon O Chua (University of California at Berkeley, USA)

Volume III continues the author’s quest for devel-oping 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 general-ized 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.

360pp Aug 2009978-981-283-793-6 US$156 £129978-981-283-794-3(ebook) US$234 £194 978-981-4468-94-7(mbook) US$62 £52


A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science (Volume IV)By (author): Leon O Chua (University of California at Berkeley, USA)

“This book is an excellent reading for students and researchers interested in nonlinear dynamics and discrete dynamical systems of one-dimensional cellular automata.”

Zentralblatt MATH

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 hy-

per (group 6) Bernoulli rules. This discovery is em-bellished 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. 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.

404pp Apr 2011978-981-4317-30-6 US$190 £158978-981-4317-31-3(ebook) US$285 £237978-981-4464-43-7(mbook) US$76 £63


A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science (Volume V)By (author): Leon O Chua (University of California at Berkeley, USA)

This penultimate volume contains numerous original, elegant, and surprising results in 1-di-mensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discov-ery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence.

But perhaps the most provocative idea is the pro-posal for adopting rule 137, over its three globally-equivalent siblings, including the heretofore more well-known rule 110, as the prototypical universal Turing machine.

352pp Mar 2012978-981-4390-51-4 US$169 £140978-981-4390-52-1(ebook) US$254 £211978-981-4397-56-8(mbook) US$68 £56

A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science

Volume I Volume II Volume III Volume IV Volume V

A Collection from Leon Chua

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World Scientific Series on Nonlinear Science Series A - Volume 4&5

Methods of Qualitative Theory in Nonlinear Dynamics (Part I and Part II)

By (author): Leonid P Shilnikov (Research In-stitute for Applied Mathematics & Cybernetics, Russia), Andrey L Shilnikov (Research Institute for Applied Mathematics & Cybernetics, Rus-sia), Dmitry V Turaev (Research Institute for Applied Mathematics & Cybernetics, Russia), Leon O Chua (UC Berkeley)

“It is well-written and clearly organized with excellent figures … This rigorous book, with its emphasis on mathematical technique, would form an excellent basis for an engineering course if supplemented with applications.”

Applied Mechanics Reviews


A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science (Volume VI)By (author): Leon O Chua (University of California at Berkeley, USA)

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 previ-ous 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.

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 par-ticular, 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 < 0), and then change the color of each cell if β < 0.

As in the five prior volumes, Vol. VI also con-tains simple recipes which are, in fact, general and original results from the abstract theory of 1-dimensional cellular automata. Indeed, both children and experts from cellular automata will find this volume to be as deep, refreshing, and entertaining, as the previous volumes.

580pp Jul 2013978-981-4460-87-3 US$145 £120978-981-4460-88-0(ebook) US$218 £181978-981-4460-89-7(mbook) US$58 £48

Volume VI

Vol.1This book is written to serve the above unful-filled need. Following the footsteps of Poin-caré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional non-linear dynamical systems. Many of the qualita-tive methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form.

416pp Dec 1998978-981-279-859-6(ebook) US$222 £183978-981-4496-42-1(mbook) US$59 £49978-981-02-3382-2 US$147 £122

Vol. 2In keeping with the self-contained nature of the book, all the topics are developed with in-troductory background and complete mathe-matical rigor. Generously illustrated and writ-ten at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics in-terested in learning a rigorous mathematical foundation of this fascinating subject.

592pp Sep 2001978-981-02-4072-1 US$183 £152978-981-279-855-8(ebook) US$275 £228978-981-4494-29-8(mbook) US$73 £61

World Scientific Series on Nonlinear Science Se-ries A - Volume 31

CNN: A Paradigm for ComplexityBy (author): Leon O Chua (UC Berkeley)

CNN is an acronym for Cellular Neural Networks when used in the context of brain science, or Cel-lular Nonlinear Networks, when used in the context of emergence and com-plexity. A CNN is mod-eled by cells and interac-tions: cells are defined as dynamical systems and interactions are defined via coupling laws. The CNN paradigm is a universal Turing machine and includes cellular automata and lattice dynamical systems as special cases. While the CNN paradigm is an example of REDUCTION-ISM par excellence, the true origin of emergence and complexity is traced to a much deeper new concept called local activity. The numerous com-plex phenomena unified under this mathematically precise principle include self organization, dissipa-tive structures, synergetics, order from disorder, far-from-thermodynamic equilibrium, collective behaviors, edge of chaos, etc.

Written with a high level of exposition, this com-pletely self-contained monograph is profusely il-lustrated with over 200 stunning color illustrations of emergent phenomena.

332pp Jun 1998978-981-02-3483-6 US$182 £151978-981-279-858-9(ebook) US$273 £227978-981-4496-13-1(mbook) US$73 £60

Local Activity Principle The Cause of Complexity and Symmetry BreakingBy (author): Klaus Mainzer (Technische Univer-sität München, Germany), Leon Chua (University of California, Berkeley, USA)

The principle of local ac-tivity explains the emer-gence of complex pat-terns in a homogeneous medium. At first defined in the theory of nonlinear electronic circuits in a mathematically rigorous way, it can be general-ized and proven at least for the class of nonlin-ear reaction–diffusion systems in physics, chemistry, biology, and brain research. Recently, it was realized by memristors for nanoelectronic device applications. In general, the emergence of complex patterns and structures is explained by symmetry breaking in homogeneous media, which is caused by local activity. This book argues that the principle of local activity is really fundamental in science, and can even be identified in quantum cosmology as symmetry breaking of local gauge symmetries generating the complexity of matter and forces in our universe. Applications are considered in economic, financial, and social systems with the emergence of equilibrium states, symmetry breaking at critical points of phase transi-tions and risky acting at the edge of chaos.

456pp Mar 2013978-1-908977-09-0 US$148 £123978-1-908977-10-6(ebook) US$222 £183978-1-908977-11-3(mbook) US$59 £49

“The book is a welcome addition to the classi-cal list of books on bifurcation theory. It is an advanced book, attempting to be more gen-eral in the abstract theory of this theory. It is very well written and contains a large number of explanatory footnotes and pictures. As such, it is very instructive even for researchers well initiated in the subject. It is also suitable as a textbook, albeit at an advanced level. Thus, it is a ‘must’ for everyone seriously interested in bifurcation theory.”

Zentralblatt MATH

A Collection from Leon Chua

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Hearts Are Poised Near the Edge of ChaosXiaohong Zhang, Zhengze Wu, Jiangxi University of Science And Technology

Leon Chua, University of California, Berkeley

The Cardiac Purkinje Fiber(CPF) is the last branch of the heart conduction system, which is meshed with the normal ventricular myocyte. Purkinje fiber plays a

key role in the occurrence of ventricular arrhythmia and maintenance. Does the heart Purkinje fiber cells have the same memory function as the cerebral nerve? In this paper, the cardiac Hodgkin-Huxley equation is taken as the object of study. In particular, we find that the potassium ion-channel K and the sodium ion-channel Na are memristors. We also derive the small-signal equivalent circuits about the equilibrium points of the CPF Hodgkin-Huxley model. According to the principle of local activity, the regions of Locally-Active domain, Edge of Chaos domain and Locally-Passive domain are partitioned under parameters (a, b), and the domain exhibiting the normal human heartbeat frequency range (Goldilocks Zone) is identi-fied. Meanwhile, the Super-Critical Hopf bifurcation of the CPF Hodgkin-Huxley model is identified. Finally, the migration changes between different state domains under external current Iext excitation are analyzed in detail.

All of the above complex nonlinear dynamics are distilled and mapped geometri-cally into a surreal union of intersecting 2-dimensional manifolds, dubbed Hodg-kin-Huxley’s magic roof .

5 Year Impact Factor: 3.395(#12 in Applied Mathematics)

3.395

International Journal of Bifurcation and Chaos (IJBC)

Best Papers of 2019Best Papers of 2019Instabilities of Nonconservative Fluid-Loaded Systems

https://doi.org/10.1142/S0218127419300398J. Michael T. Thompson and Lawrence N. Virgin

Exact Traveling Wave Solutions and Bifurcations of Classical and Modified Serre Shallow Water Wave

Equationshttps://doi.org/10.1142/S0218127419501530

Jibin Li, Guanrong Chen and Jie Song

A Holling-Tanner Predator-Prey Model with Strong Allee Effect

https://doi.org/10.1142/S0218127419300325Claudio Arancibia-Ibarra, José D. Flores, Graeme Pettet

and Peter van Heijster

The Chesnavich Model for Ion-Molecule Reactions: A Rigid Body Coupled to a Particle

https://doi.org/10.1142/S0218127419500251Gregory S. Ezra and Stephen Wiggins

Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic

Dynamicshttps://doi.org/10.1142/S0218127419501578

Vladimír Krajnák and Stephen Wiggins

Exotic Patterns of Synchrony in Planar Lattice Networkshttps://doi.org/10.1142/S0218127419300039

Ian Stewart

(#12 in Applied Mathematics)

Best Papers of 2019

a collection from leon chua - world scientific

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