Advanced topics on cellular self-organizing nets and chaotic nonlinear dynamics to model and control complex systems
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 introducin...
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| Main Authors | , , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
New Jersey
World Scientific Publishing Co. Pte. Ltd
2008
World Scientific World Scientific Publishing Company WORLD SCIENTIFIC WSPC |
| Edition | 1 |
| Series | Nonlinear Science, Series A: Monographs and Treatises |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9789812814043 9812814043 9812814051 9789812814050 |
| DOI | 10.1142/6830 |
Cover
Table of Contents:
- Advanced topics on cellular self-organizing nets and chaotic nonlinear dynamics to model and control complex systems -- Preface -- Contributors -- List of People Involved in the FIRB Project -- Contents -- Chapter 1: The CNN Paradigm for Complexity -- Chapter 2: Emergent Phenomena in Neuroscience -- Chapter 3: Frequency Analysis and Identification in Atomic Force Microscopy -- Chapter 4: Control and Parameter Estimation of Systems with Low-Dimensional Chaos - The Role of Peak-to-Peak Dynamics -- Chapter 5: Synchronization of Complex Networks -- Chapter 6: Economic Sector Identification in a Set of Stocks Traded at the New York Exchange: A Comparative Analysis -- Chapter 7: Innovation Systems by Nonlinear Networks -- Index.
- 3.3 Frequency Analysis via Harmonic Balance -- 3.3.1 Piecewise interaction model analysis -- 3.3.2 Lennard Jones-like hysteretic model analysis -- 3.4 Identification of the Tip-Sample Force Model -- 3.4.1 Identification method -- 3.4.2 Experimental results -- 3.5 Conclusions -- References -- 4. Control and Parameter Estimation of Systems with Low-Dimensional Chaos - The Role of Peak-to-Peak Dynamics -- 4.1 Introduction -- 4.2 Peak-to-Peak Dynamics -- 4.3 Control System Design -- 4.3.1 PPD modeling and control -- 4.3.2 The impact of noise and sampling frequency -- 4.3.3 PPD reconstruction -- 4.4 Parameter Estimation -- 4.4.1 Derivation of the "empirical PPP" -- 4.4.2 Interpolation of the "empirical PPP" -- 4.4.3 Optimization -- 4.4.4 Example of application -- 4.5 Concluding Remarks -- References -- 5. Synchronization of Complex Networks -- 5.1 Introduction -- 5.2 Synchronization of Interacting Oscillators -- 5.3 From Local to Long-Range Connections -- 5.4 The Master Stability Function -- 5.4.1 The case of continuous time systems -- 5.4.2 The Master stability function for coupled maps -- 5.5 Key Elements for the Assessing of Synchronizability -- 5.5.1 Bounding the eigenratio -- 5.5.2 Other approaches for assessing synchronizability -- 5.6 Synchronizability of Weighted Networks -- 5.6.1 Coupling matrices with a real spectra -- 5.6.2 Numerical simulations -- 5.6.3 Weighting: local vs global approaches -- 5.6.4 Coupling matrices with a complex spectra -- 5.6.5 Essential topological features for synchronizability -- 5.7 Synchronization of Coupled Oscillators: Some Significant Results -- 5.7.1 Networks of phase oscillators -- 5.7.2 Networks of coupled oscillators -- 5.8 Conclusions -- References -- 6. Economic Sector Identification in a Set of Stocks Traded at the New York Exchange: A Comparative Analysis -- 6.1 Introduction -- 6.2 The Data Set
- 6.3 Random Matrix Theory -- 6.4 Hierarchical Clustering Methods -- 6.4.1 Single linkage correlation based clustering -- 6.4.2 Average linkage correlation based clustering -- 6.5 The Planar Maximally Filtered Graph -- 6.6 Conclusions -- References -- 7. Innovation Systems by Nonlinear Networks -- 7.1 Introduction -- 7.2 Cellular Automata Model -- 7.3 Innovation Models Based on CNNs -- 7.4 Simulation Results -- 7.5 Conclusions -- References -- Index
- Intro -- Contents -- Preface -- Contributors -- List of People Involved in the FIRB Project -- 1. The CNN Paradigm for Complexity -- 1.1 Introduction -- 1.2 The 3D-CNN Model -- 1.3 E3: An Universal Emulator for Complex Systems -- 1.4 Emergence of Forms in 3D-CNNs -- 1.4.1 Initial conditions -- 1.4.2 3D waves in homogeneous and unhomogeneous media -- 1.4.3 Chua's circuit -- 1.4.4 Lorenz system -- 1.4.5 Rössler system -- 1.4.6 FitzHugh-Nagumo neuron model -- 1.4.7 Hindmarsh-Rose neuron model -- 1.4.8 Inferior-Olive neuronmodel -- 1.4.9 Izhikevich neuronmodel -- 1.4.10 Neuron model exhibiting homoclinic chaos -- 1.5 Conclusions -- 2. Emergent Phenomena in Neuroscience -- 2.1 Introductory Material: Neurons and Models -- 2.1.1 Models of excitability -- 2.1.2 The Hodgkin-Huxley model -- 2.1.3 The FitzHugh-Nagumo model -- 2.1.4 Class I and class II excitability -- 2.1.5 Other neuronmodels -- 2.2 Electronic Implementation of NeuronModels -- 2.2.1 Implementation of single cell neuron dynamics -- 2.2.2 Implementation of systems with many neurons -- 2.3 Local Activity Theory for Systems of IO Neurons -- 2.3.1 The theory of local activity for one-port and two-port systems -- 2.3.2 The local activity and the edge of chaos regions of the inferior olive neuron -- 2.4 Simulation of IO Systems: Emerging Results -- 2.4.1 The paradigm of local active wave computation for image processing -- 2.4.2 Local active wave computation based paradigm: 3D-shape processing -- 2.5 Networks of HR Neurons -- 2.5.1 The neural model -- 2.5.2 Parameters for dynamical analysis -- 2.5.3 Dynamical effects of topology on synchronization -- 2.6 Neurons in Presence of Noise -- 2.7 Conclusions -- 3. Frequency Analysis and Identification in Atomic Force Microscopy -- 3.1 Introduction -- 3.2 AFM Modeling -- 3.2.1 Piecewise interaction force -- 3.2.2 Lennard Jones-like interaction force