Local Activity Principle: The Cause Of Complexity And Symmetry Breaking

by Klaus Mainzer, Leon O Chua

Overview

The principle of local activity explains the emergence of complex patterns in a homogeneous medium. At first defined in the theory of nonlinear electronic circuits in a mathematically rigorous way, it can be generalized and proven at least for the class of nonlinear 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 transitions and risky acting at the edge of chaos.

Product Details

ISBN-13:	9781908977090
Publisher:	Imperial College Press
Publication date:	05/06/2013
Pages:	456
Product dimensions:	6.70(w) x 9.80(h) x 0.90(d)

Table of Contents

Preface vii

1 The Local Activity Principle and the Emergence of Complexity 1

1.1 Mathematical Definition of Local Activity 1

1.2 The Local Activity Theorem 9

1.3 Local Activity is the Origin of Complexity 15

2 Local Activity and Edge of Chaos in Computer Visualization 23

2.1 Local Activity and Edge of Chaos of the Brusselator Equations 23

2.2 Local Activity and Edge of Chaos of the Gierer-Meinhardt Equations 35

2.3 Local Activity and Edge of Chaos of the FitzHugh-Nagumo Equations 48

2.4 Local Activity and Edge of Chaos of the Hodgkin-Huxley Equations 75

2.5 Local Activity and Edge of Chaos of the Oregonator Equations 84

3 The Local Activity Principle and the Expansion of the Universe 105

3.1 Mathematical Definition of Symmetry 105

3.2 Symmetries in the Quantum World 107

3.3 Global and Local Symmetries 108

3.4 Local Gauge Symmetries and Symmetry Breaking 115

4 The Local Activity Principle and the Dynamics of Matter 147

4.1 The Local Activity Principle of Pattern Formation 147

4.2 The Local Activity Principle and Prigogine's Dissipative Structures 149

4.3 The Local Activity Principle and Haken's Synergetics 165

5 The Local Activity Principle and the Evolution of Life 171

5.1 The Local Activity Principle of Turing's Morphogenesis 172

5.2 The Local Activity Principle in Systems Biology 174

5.3 The Local Activity Principle in Brain Research 192

6 The Local Activity Principle and the Co-evolution of Technology 205

6.1 The Local Activity Principle of Cellular Automata 205

6.2 The Local Activity Principle of Neural Networks 269

6.3 The Local Activity Principle of Memristors 287

6.4 The Local Activity Principle of Global Information Networks 312

7 The Local Activity Principle and Innovation in the Economy and Society 327

7.1 The Local Activity Principle in Sociodynamics 328

7.2 The Local Activity Principle and Emerging Risks 338

7.3 The Local Activity Principle in Financial Dynamics 355

7.4 The Local Activity Principle in Innovation Dynamics 376

7.5 The Local Activity Principle of Sustainable Entrepreneurship 386

8 The Message of the Local Activity Principle 393

8.1 The Local Activity Principle in Culture and Philosophy 394

8.2 What can we Learn from the Local Activity Principle in the Age of Globalization? 406

References 409

Author Index 423

Subject Index 425