This book focuses on the research topics investigated during the three-year research project funded by the Italian Ministero dell Istruzione, dell Università e della Ricerca (MIUR: Ministry of Education, University and Research) under the FIRB project RBNE01CW3M. With the aim of introducing newer perspectives of the research on complexity, the final results of the project are presented after a general introduction to the subject. The book is intended to provide researchers, PhD students, and people involved in research projects in companies with the basic fundamentals of complex systems and the advanced project results recently obtained.
Contents: The CNN Paradigm for Complexity; Emergent Phenomena in Neuroscience; Frequency Analysis and Identification in Atomic Force Microscopy; Control and Parameter Estimation of Systems with Low-Dimensional Chaos -- The Role of Peak-to-Peak Dynamics; Synchronization of Complex Networks; Economic Sector Identification in a Set of Stocks Traded at the New York Exchange: A Comparative Analysis; Innovation Systems by Nonlinear Networks.
Author(s): Riccardo Caponetto
Series: World Scientific Series on Nonlinear Science
Publisher: World Scientific Publishing Company
Year: 2008
Language: English
Pages: 208
Contents......Page 14
Preface......Page 6
Contributors......Page 8
List of People Involved in the FIRB Project......Page 12
1.1 Introduction......Page 18
1.2 The 3D-CNN Model......Page 20
1.3 E3: An Universal Emulator for Complex Systems......Page 26
1.4 Emergence of Forms in 3D-CNNs......Page 29
1.4.1 Initial conditions......Page 30
1.4.2 3D waves in homogeneous and unhomogeneous media......Page 31
1.4.3 Chua’s circuit......Page 33
1.4.4 Lorenz system......Page 34
1.4.6 FitzHugh-Nagumo neuron model......Page 37
1.4.7 Hindmarsh-Rose neuron model......Page 38
1.4.8 Inferior-Olive neuronmodel......Page 39
1.4.9 Izhikevich neuronmodel......Page 43
1.4.10 Neuron model exhibiting homoclinic chaos......Page 44
1.5 Conclusions......Page 46
2.1 Introductory Material: Neurons and Models......Page 56
2.1.1 Models of excitability......Page 57
2.1.2 The Hodgkin-Huxley model......Page 58
2.1.3 The FitzHugh-Nagumo model......Page 59
2.1.4 Class I and class II excitability......Page 60
2.1.5 Other neuronmodels......Page 61
2.2 Electronic Implementation of NeuronModels......Page 63
2.2.1 Implementation of single cell neuron dynamics......Page 64
2.2.2 Implementation of systems with many neurons......Page 66
2.3 Local Activity Theory for Systems of IO Neurons......Page 71
2.3.1 The theory of local activity for one-port and two-port systems......Page 72
2.3.2 The local activity and the edge of chaos regions of the inferior olive neuron......Page 73
2.4.1 The paradigm of local active wave computation for image processing......Page 75
2.4.2 Local active wave computation based paradigm: 3D-shape processing......Page 77
2.5 Networks of HR Neurons......Page 80
2.5.1 The neural model......Page 81
2.5.2 Parameters for dynamical analysis......Page 83
2.5.3 Dynamical effects of topology on synchronization......Page 85
2.6 Neurons in Presence of Noise......Page 89
2.7 Conclusions......Page 96
3.1 Introduction......Page 100
3.2 AFM Modeling......Page 102
3.2.2 Lennard Jones-like interaction force......Page 105
3.3 Frequency Analysis via Harmonic Balance......Page 106
3.3.1 Piecewise interaction model analysis......Page 108
3.3.2 Lennard Jones-like hysteretic model analysis......Page 110
3.4.1 Identification method......Page 112
3.5 Conclusions......Page 115
References......Page 116
4.1 Introduction......Page 118
4.2 Peak-to-Peak Dynamics......Page 119
4.3 Control System Design......Page 122
4.3.1 PPD modeling and control......Page 123
4.3.2 The impact of noise and sampling frequency......Page 126
4.3.3 PPD reconstruction......Page 127
4.4 Parameter Estimation......Page 132
4.4.1 Derivation of the “empirical PPP”......Page 133
4.4.3 Optimization......Page 134
4.4.4 Example of application......Page 135
References......Page 138
5.2 Synchronization of Interacting Oscillators......Page 140
5.3 From Local to Long-Range Connections......Page 142
5.4.1 The case of continuous time systems......Page 143
5.4.2 The Master stability function for coupled maps......Page 148
5.5 Key Elements for the Assessing of Synchronizability......Page 149
5.5.1 Bounding the eigenratio......Page 150
5.5.2 Other approaches for assessing synchronizability......Page 151
5.6.1 Coupling matrices with a real spectra......Page 152
5.6.2 Numerical simulations......Page 154
5.6.3 Weighting: local vs global approaches......Page 156
5.6.4 Coupling matrices with a complex spectra......Page 157
5.6.5 Essential topological features for synchronizability......Page 160
5.7.1 Networks of phase oscillators......Page 162
5.7.2 Networks of coupled oscillators......Page 165
References......Page 168
6.1 Introduction......Page 176
6.2 The Data Set......Page 178
6.3 Random Matrix Theory......Page 179
6.4 Hierarchical Clustering Methods......Page 182
6.4.1 Single linkage correlation based clustering......Page 183
6.4.2 Average linkage correlation based clustering......Page 186
6.5 The Planar Maximally Filtered Graph......Page 191
6.6 Conclusions......Page 195
References......Page 196
7.1 Introduction......Page 198
7.2 Cellular Automata Model......Page 200
7.3 Innovation Models Based on CNNs......Page 201
7.4 Simulation Results......Page 203
7.5 Conclusions......Page 204
References......Page 205
Index......Page 206
