Hjem

Preface
Chapter 1 Introduction to nonlinear systems
1.1 Classification of complex systems
1.2 First-order systems
1.3 Numerical solutions of differential equations
1.4 Exercises
Chapter 2 The logistic map and elements of complex system dynamics
2.1 The logistic map
2.2 Equilibrium points and periodic solutions of the logistic map
2.3 Chaos in the logistic map
2.4 Intermittency
2.5 Bifurcation diagram and Feigenbaum constant
2.6 Characterizing elements of chaotic behavior
2.6.1 Lyapunov exponents
2.7 Exercises
Chapter 3 Bifurcations
3.1 Introduction to bifurcations in dynamical systems
3.2 Elementary bifurcations
3.3 Bifurcations towards catastrophes
3.4 Exercises
Chapter 4 Oscillators
4.1 Hopf bifurcation
4.2 Examples of oscillations and oscillators
4.3 Genesis of electronic oscillators
4.4 Li´enard systems
4.5 Dynamics of the van der Pol oscillator
4.6 Lur'e systems and the design of oscillators
4.7 Describing functions: essential elements
4.8 Hewlett oscillator
4.9 2D maps
4.10 Summary
4.11 Exercises
Chapter 5 Strange attractors and continuous-time chaotic systems
5.1 Features of chaos in continuous-time systems
5.2 Genesis of chaotic oscillations: the Chua's circuit
5.3 Canonical chaotic attractors and their bifurcation diagrams
5.4 Further essential aspects of chaotic systems
5.5 Chaotic dynamics in Lur'e systems
5.6 Hyperchaotic circuits
5.7 Summary
5.8 Exercises
Chapter 6 Cellular Nonlinear Networks
6.1 CNN: basic notations
6.2 CNNs: main aspects
6.3 Cloning templates and features of CNNs
6.4 The CNN as a generator of nonlinear dynamics
6.5 Reaction-diffusion CNN
6.6 Summary
6.7 Exercises
Chapter 7 Synchronization and chaos control
7.1 Introduction
7.2 Principles of synchronization of nonlinear dynamical systems
7.3 Schemes for unidirectional synchronization
7.4 Synchronization via diffusive coupling
7.5 Principles of chaos control
7.6 Strategies for chaos control
7.7 General remarks on chaos control
7.8 Exercises
Chapter 8 Experiments and applications
8.1 Hewlett oscillator
8.2 Van der Pol oscillator
8.3 An "elegant" oscillator
8.4 Synchronization of two Hewlett oscillators
8.5 Multilayer CNN cell with slow-fast dynamics for RD-CNN
8.6 Non-autonomous multilayer CNN with chaotic behavior
8.7 Multilayer SC-CNN with Chua's circuit dynamics
8.8 Multilayer SC-CNN implementing hyperchaotic Chua's circuit dynamics
8.9 A SC-CNN chaotic circuit with memristor
8.10 Synchronization of two Chua's dynamics with diffusive coupling
8.11 Chaos encryption
8.12 Qualitative chaos-based sensors
8.13 Chaos control experiment
8.14 Logistic map with Arduino
8.15 Networks of SC-CNN Chua's circuits
8.16 Exercises Bibliography Index