by Leon O Chua (University of California, Berkeley)

Table of Contents (73k)
Preface (99k)
Introduction (163k)
Chapter 1: What is a CNN? (2,246k)

Leon O Chua is Professor of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He has written and co-authored several books on nonlinear science, mathematics, and engineering, including Introduction to Nonlinear Network Theory (McGraw-Hill), Practical Numerical Algorithms for Chaotic Systems (Springer-Verlag) and Methods of Qualitative Theory in Nonlinear Dynamics (World Scientific), and is the Editor of the International Journal of Bifurcation and Chaos. Prof. Chua has received several awards and honors, including six USA patents, seven honorary doctorates (docteur honoris causa) and has been elected a foreign member of the European Academy of Sciences (Academia Europaea).
 

Revolutionary and original, this treatise presents a new paradigm of EMERGENCE and COMPLEXITY, with applications drawn from numerous disciplines, including artificial life, biology, chemistry, computation, physics, image processing, information science, etc.

CNN is an acronym for Cellular Neural Networks when used in the context of brain science, or Cellular Nonlinear Networks, when used in the context of emergence and complexity. A CNN is modeled by cells and interactions: 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 REDUCTIONISM par excellence, the true origin of emergence and complexity is traced to a much deeper new concept called local activity. The numerous complex phenomena unified under this mathematically precise principle include self organization, dissipative structures, synergetics, order from disorder, far-from-thermodynamic equilibrium, collective behaviors, edge of chaos, etc.

Written with a high level of exposition, this completely self-contained monograph is profusely illustrated with over 200 stunning color illustrations of emergent phenomena.

• What is a CNN?
• Standard CNNs:
  • Standard CNNs are Uniquely Specified by CNN Genes
  • Oscillations and Chaos from Standard CNNs
  • Complete Stability Criteria for Standard CNNs
  • Bistable Criterion
  • Coding the CNN Gene
  • A Gallery of Basic CNN Genes
  • Does There Exist a CNN Gene for Solving Minsky's Global Connectivity Problem?
  • Decoding the CNN Gene
  • What Task Can an Uncoupled Boolean CNN Gene Perform?
  • Bifurcation of CNN Genes
  • The Game-of-Life CNN Gene
  • The CNN Universal Machine
  • Generalized Cellular Automata
  • A Glimpse at Some Real-World CNN Applications
• Autonomous CNNs:
  • Pattern Formation in Standard CNNs
  • Pattern Formation in Reaction-Diffusion CNNs
  • Nonlinear Waves in Reaction-Diffusion CNNs
  • Simulating Nonlinear PDEs via Autonomous CNNs
• Local Activity: The Genesis of Complexity:
  • Transistors and Local Activity: What Do They Have in Common?
  • Nonlinear Circuit Models for Reaction-Diffusion CNNs
  • What is Local Activity?
  • Testing for Local Activity
  • Why is Local Activity Necessary for Pattern Formation?
  • How to Choose Locally-Active CNN Parameters?
  • Local Activity and Stability are Different Concepts
  • The Local Activity Dogma