Contents
1.1Linear, Nonlinear, and Chaos
1.3Famous Scientists and Important Events
1.3.1Lorenz and Butterfly Effect
1.3.2Li Tien-Yien and the Concept of Chaos
1.3.3Feigenbaum and Feigenbaum Constant
1.3.4Leon Ong Chua and Chua’s Circuit
1.3.5Guanrong Chen and Chen’s Attractor
1.4Definition and Characteristics of Chaos
1.5Overview of Chaos Synchronization Method
1.5.1Chaos Synchronization Methods and Characteristics
1.5.2Other Synchronization Methods and Problems
1.6Summary of Chaos Secure Communication
1.6.1Chaotic Analog Communication
1.6.2Chaotic Digital Communication
1.6.3Encryption Communication based on Chaotic Sequence
1.7Chaos Research Methods and Main Research Contents
2Characteristic Analysis Methods for Nonlinear System
2.1Phase Diagram Analysis Method
2.2Power Spectral Analysis Method
2.4Lyapunov Characteristic Exponent Method
2.4.1Definition of Lyapunov Characteristic Exponent
2.4.2Lyapunov Exponent Spectrum
2.4.3Physical Meaning of Lyapunov Exponent
2.4.4Condition Lyapunov Exponent
2.5Fractal Dimension Analysis Method
2.6.2Improved 0–1 Test Algorithm
2.6.3Application of 0–1 Test Algorithm
2.7Dividing Frequency Sampling Method
2.9Complexity Measure Algorithm
2.9.1Spectral Entropy Complexity Algorithm
3.1.4Tangent Delay-Ellipse Reflecting Cavity System Map
3.2Continuous-Time Chaotic System
3.2.10Standard for a New Chaotic System
3.3.1Rössler Hyperchaotic System
3.3.3Folded Towel Hyperchaotic Map
4Chaotic Synchronization Principle and Method
4.1Definition of Chaos Synchronization
4.2Performance Index of Chaotic Synchronization System
4.3Principle and Performance of Feedback Control Synchronization
4.3.1Multivariable drive feedback synchronization for chaotic system
4.3.2Linear and Nonlinear Feedback Synchronization for Discrete Chaotic System
4.4Parameter Adaptive Synchronization Based on Pecora–Carroll Synchronization Criterion
4.4.1Principle for Adaptive Synchronization
4.4.2Choose Control Law and Control Parameters
4.4.3Determine the Boundary and Range of the Control Constant
4.4.4Simulation Results and Discussion
4.5Adaptive Synchronization Control Based on Lyapunov Stable Theory
4.5.1Adaptive Synchronization Control with Certain Parameter
4.5.2Adaptive Synchronization Control with Uncertain Parameters
4.6Intermittent Feedback Synchronization Control
4.6.1Intermittent Synchronization Control between Different Systems
4.6.2Synchronization Simulation and Performance Analysis
4.7Synchronization Control Based on State Observer Method
4.7.1Design Principle of State Observer
4.7.2Design of State Observer for Unified Chaotic System
4.7.3Simulation and Discussion
4.8Chaos Synchronization Based on Chaos Observer
4.8.1Design Principle of Chaos Observer
4.8.2Chaos Observer of the Unified Chaotic System
4.8.3Synchronization Simulation and Performance Analysis
4.9.1Principle and Simulation of Proportional Projection Synchronization
4.9.2Principle and Simulation of Function Projective Synchronization
4.9.3Principle and Simulation of the Adaptive Function Projective Synchronization
4.10Problems and Development of Chaos Synchronization
5Secure Communication Technology Based on Chaos Synchronization
5.1Chaotic Masking Communication
5.2Chaos Shift Keying Communication
5.4Chaotic Spread Spectrum Communication
5.4.1Principle of Chaotic DS/SS Communication
5.4.2Generation of Chaotic Spread Spectrum Code
5.4.3Simulation Module Design of Multiuser Chaotic Spread Spectrum System
5.4.4Design and Simulation of Multiuser Chaotic Spread Spectrum System Based on Rake Receiver
5.4.5Performance Analysis of Multiuser Chaotic Spread Spectrum System Based on Rake Receiver
6Data Encryption Based on Chaotic Sequence
6.1.2Relationship between Chaos Cryptography and Traditional Cryptography
6.1.3Principle of Chaos Sequence Encryption
6.2Data Encryption Algorithm Based on Chaotic Sequence
6.2.1Basic Requirements of Chaotic Encryption Algorithm
6.2.2Logistic Map and Its Statistics
6.2.3Chaotic Encryption Model and Algorithm
6.2.4Implement of Encryption Algorithm Based on Chaotic Sequence
6.2.5System Performance Analysis
6.3Binary Watermark Image Encryption Algorithm Based on Chaos
6.3.1Improvement of Chaotic Pseudo-Random Sequence Generator
6.3.2Binary Watermark Image Encryption Algorithm Based on TD-ERCS Map
6.3.3Performance Analysis of Encryption Algorithm
6.4Color Image Watermarking Algorithm Based on Chaotic Map and Wavelet Transform
6.4.1Wavelet Transformation Algorithm and Its Application
6.4.2Design and Implementation of Watermark Embedding and Extraction Algorithm
6.4.3Simulation and Performance Analysis
6.5Chaotic Image Encryption Algorithm
6.5.1Chaos-Based Image Encryption Technology
6.5.2A New Chaotic Image Encryption Scheme
7Audio and Video Chaotic Encryption and Communication Technology
7.1Principle of Real-Time Voice Encryption Communication
7.1.1Principle of Digital Encryption Communication System
7.1.2Real-Time Voice Encryption and Communication System
7.1.3Cipher Synchronization Technology
7.2Real-Time Data Stream Encryption Algorithm
7.2.13DES Encryption Algorithm
7.2.2Encryption Algorithm Based on 3DES and Chaotic Map
7.2.3Network Synchronization Method
7.2.4Security Analysis of Real-Time Voice Encryption System
7.3Realization of Real-Time Voice Encryption System
7.3.1Structure of Real-Time Voice Encryption System
7.3.2Real-Time Transmission Protocol and Its Data Structure
7.3.3Implementation of RTP Based on Adaptive Communication Environment
7.3.4System Debugging and Performance Testing
7.4MPEG Video Encryption Algorithm Based on Chaotic Sequence
7.4.1Encryption Principle and Procedure of MPEG Video Data
7.4.2Design of Stream Cipher Based on Chaos
7.4.3Design of Scrambling Algorithm Based on Chaos
7.4.4Encryption Experiment and Encryption Effect Analysis
7.4.5Performance Analysis of MPEG Video Encryption System
7.5H.264 Video Encryption Algorithm Based on Chaos
7.5.1Chaotic Stream Cipher Based on Tangent Delay-Ellipse Reflecting Cavity System
7.5.2H.264 Video Encryption Scheme
7.5.3Performance Analysis of Video Encryption
8Analysis and Simulation of Fractional-Order Chaotic System
8.1Development of Fractional-Order Chaotic System
8.2Definition and Physical Meaning of Fractional Calculus
8.3Solution Methods of Fractional-Order Chaotic System
8.3.1Frequency Domain Method for Solving Fractional-Order Chaotic System
8.3.2Time Domain Method for Solving Fractional-Order Chaotic System
8.4Simulation Method for Fractional-Order Chaotic System
8.4.1Dynamic Simulation Method for Fractional-Order Chaotic System
8.4.2Circuit Simulation Method of Fractional-Order Chaotic System
8.4.3Numerical Simulation Method of Fractional-Order Chaotic System
8.4.4Comparison of Simulation Methods
8.5Dynamics of Fractional-Order Unified System Based on Frequency Domain Method
8.5.1Fractional-Order Unified Chaotic System Mode
8.5.2Dynamic Simulation of Fractional-Order Unified Chaotic System
8.5.3Dynamics of Fractional-Order Unified System with Fixed Parameter
8.5.4Dynamics of Fractional-Order Unified System with Different Parameter
8.6Dynamics of Fractional-Order Diffusionless Lorenz System Based on Time Domain Method
8.6.1Fractional-Order Diffusionless Lorenz System Model
8.6.2Chaotic Characteristic of Fractional-Order Diffusionless Lorenz System
8.6.3Bifurcation Analysis with Varying System Parameter R
8.6.4Bifurcation Analysis with Varying Fractional Order q
8.6.5Bifurcations with Different Fractional Order
9Simulation and Hardware Implementation of Chaotic System
9.1Dynamic Simulation of Chaotic System
9.1.1Dynamic Simulation Steps on Simulink
9.1.2Simulation Result Analysis and Performance Improvement
9.2Circuit Simulation of Chaotic System
9.3Design of Chaotic Analog Circuit
9.3.1Procedure of Chaotic Circuit Design
9.3.2Modular Design of Chaotic Circuit
9.3.3Basic Components of Chaotic Circuit
9.4Improved Modular Design of Chaotic Circuit
9.4.1Design of Multiscroll Jerk Circuit Based on OA
9.4.2Design of Multiscroll Jerk Circuit Based on CC
9.4.3Multiscroll Jerk Circuit Implementation
9.5Digital Signal Processor Design and Implementation of Chaotic Systems
9.5.1DSP Experimental Platform of Chaotic System
9.5.2DSP Implementation of Integer-Order Chaotic System
9.5.3DSP Implementation of Fractional-Order Chaotic System
Appendix A:Important Academic Journals in the Field of Chaos
Appendix B:Matlab Source Programs of Chaos Characteristic Analysis
B.1Mode of the Simplified Lorenz System
B.2Programs about Characteristic Analysis of Integer-Order Simplified Lorenz System
B.2.1Simulation Codes for Matlab Toolbox with Runge–Kutta Algorithm
B.2.2Solution Based on Euler and Runge–Kutta Algorithm
B.2.3Program of Calculating LE
B.2.4Program of Calculating the Maximum LE
B.2.5Program for Calculating Bifurcation Diagram
B.2.6Program for Plotting Poincaré Section
B.3Solution Program for the Fraction-Order Simplified Lorenz System
B.3.1Solution Program Based on Predictor–Corrector Approach
B.3.2Solution Program Based on Adomian Decomposition Approach
B.3.3Analysis Program of Complexity and Chaos Diagram
B.4Simulation of Chaotic Synchronization