Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications (Emerging Methodologies and Applications in Modelling, Identification and Control)

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Recent Advances
in Chaotic Systems
and Synchronization:
From Theory to Real World Applications
Copyright
Contributors
Preface
Part I: New Chaotic Systems: Design and Analysis
1
Experimental Observations and Circuit Realization of a Jerk Chaotic System With Piecewise Nonlinear Function
	Introduction
	Mathematical Model and Basic Properties
	Dynamic Analysis
		Equilibrium and Stability
		Routes to Chaos
		Lyapunov Exponents Analysis
		Comparative Analysis
	Circuit Design
	Experimental Results
	Conclusion
	References
2
Analytical, Numerical and Experimental Analysis of an RC Autonomous Circuit With Diodes in Antiparallel
	Introduction
	Analysis of Autonomous RC Circuit With Diodes in Antiparallel
		Symmetry, Invariance, Dissipative Character, and Linear Stability of the Equilibrium Points
		Dynamical Behaviors of the Circuit
			Routes to Chaos With Respect to Parameter a
			Routes to Chaos to Parameter b
			Routes to Chaos With Respect to Parameter d
		Observation of Chaotic Attractors From the Oscilloscope
	Conclusion
	References
3
Chaos in a System With Parabolic Equilibrium
	Introduction
	Model of a System With Infinite Equilibria
	Dynamical Properties of the System With Parabolic Equilibrium
		Equilibrium Points and Stability
		Dynamical Behavior
	Circuitry Implementation of the System With Parabolic Equilibrium
	Adaptive Control of the System With Parabolic Equilibrium
	Adaptive Synchronization of Two Systems With Parabolic Equilibrium
	Discussion
	Conclusion
	References
4
A New Four-Dimensional Chaotic System With No Equilibrium Point
	Introduction
	New No Equilibrium Chaotic System
	Fractional Order Hyperjerk System (FOHJS)
		Bifurcation
	Circuit Design
	Conclusion
	References
5
A New Five Dimensional Multistable Chaotic System With Hidden Attractors
	Introduction
	New System and Its Dynamical Properties
	Digital Implementation for the System Using Field Programmable Gate Arrays
	Analog Circuit Design
	Conclusion
	References
6
Extreme Multistability in a Hyperjerk Memristive System With Hidden Attractors
	Introduction
	The Hyperjerk Memristive System
	System's Extreme Multistability
	Conclusion
	References
	Further Reading
7
Parameter Estimation of Chaotic Systems Using Density Estimation of Strange Attractors in the State Space
	Introduction
	A New Chaotic System and Its Bifurcation Analysis
	Density Estimation of the Attractor in the State Space Using GMM
		Initialization Step
		Expectation Step
		Maximization Step
		Likelihood Score Evaluation
		Determining the Appropriate Number of Gaussian Components
	Parameter Estimation of the Chaotic System Using GMM-Based Cost Functions
		Learning Phase
		Evaluation Phase
	Simulation Results
		The GMM of the Chaotic System
		1D Parameter Estimation of the Chaotic System
		The Effect of the Length of the Evaluation Data
		2D Parameter Estimation of the Chaotic System
	Conclusion
	References
Part II: Real World Applications
8
Virtualization of Chua's Circuit State Space
	Introduction
	Chuas Circuit
	Boundary Surface
	Virtual Reality and Other Visualization Forms
		3D Virtualization Sequence and Its Implementation
		Input Data Preparation and Acquisition
		Modeling, Editing and Verification
		Visualization and Working With Virtual World
		3D Display Systems
		3D Printing and Real Objects Creation
	Visualization and Immersive Environments
		Mixed Reality System Implementation
		CAVE System Implementation
	Visualization of Objects in State Space
		Visualization of a Chaotic Attractor by Software Means
		Visualization of BS
		Visualization in Virtual Cave Environment
	Possibilities of Calculation of C-SBS
		Calculation of C-SBS by a PC With Single or Multicore Processor
		GRID Technology or High-Performance Computer Clusters
		GPGPU Technology Usage
	Conclusion
	References
9
Some New Chaotic Maps With Application in Stochastic
	Introduction
	One-dimensional White Gaussian Noise Generator
	Attention Deficit Disorder Model
	Discussion and Conclusion
	References
10
Chaotic Solutions in a Forced Two-Dimensional Hindmarsh-Rose Neuron
	Introduction
	Model and Description
	Numerical Results of the Bifurcation Analysis
	Numerical Results of Wave Propagation in the Designed Network
	Conclusion
	References
11
PD Bifurcation and Chaos Behavior in a Predator-Prey Model With Allee Effect and Seasonal Perturbation
	Introduction
	Mathematical Modeling
	Preliminaries
	Dynamical Analysis of System for Both Types of Allee Effect
	Numerical Analysis
		Predator-Prey System With Strong Allee Effect
		Predator-Prey System With Weak Allee Effect Case Study
		Seasonally Perturbed System
	Conclusion
	References
12
Chaotic Path Planning for a Two-Link Flexible Robot Manipulator Using a Composite Control Technique
	Introduction
	Modeling of the Two-Link Flexible Manipulator
	Singular Perturbation Modeling of a TLFM
		Dynamic Model of the Slow Subsystem
		Dynamic Model of the Fast Subsystem
	Design of a Composite Control
		Dynamic Surface Control of the Slow Subsystem
		Backstepping Control for the Fast Subsystem
	Chaotic Signal as the Desired Trajectory
	Results and Discussion for the Composite Control
	Simulation Results With the Nominal Payload (0.145kg)
	Chaotic Trajectory Tracking With a 0.3 kg Payload
	Conclusions
	References
Part III: New Trends in Chaos Synchronization
13
Robust Synchronization of Master Slave Chaotic Systems: A Continuous Sliding-Mode Control Approach With Exper ...
	Introduction
	Preliminaries
	Problem Statement
	Output-Feedback-Based Continuous Singular Terminal Sliding-Mode (CSTSM) Controller Design
		Finite-Time Sliding-Mode Observer
	Numerical Simulation Results
	Experimental Study
	Conclusion
	References
14
A Four-Dimensional Chaotic System With One or Without Equilibrium Points: Dynamical Analysis and Its Applicat ...
	Introduction
	Model of Proposed Autonomous System With One or Without Equilibrium Points
	Dynamical Analysis of Proposed Autonomous System With One or Without Equilibrium Points
		Self-Excited Attractor in Proposed Autonomous System With Only One Equilibrium Point
		Hidden Attractor in Proposed Autonomous System Without Equilibrium Point
	Electronic Circuit Implementation of Proposed Autonomous System With One or Without Equilibrium Points
	Adaptive Finite-Time Synchronization of Proposed Autonomous System With Hidden Attractor
		Preliminaries
		Main Results
		Numerical Verifications
	A Text Encryption Application Using Hidden Chaotic Attractor of Proposed Autonomous System With One or Without Equilib ...
		Proposed Affine Cipher
		Key Generation
		Numerical Verifications
	Concluding Remarks
	References
15
FPGA Implementation of Chaotic Oscillators, Their Synchronization, and Application to Secure Communications
	Introduction
	Simulation of Chaotic Oscillators Based on PWL Functions
		Numerical Methods to Simulate Chaotic Oscillators
		Simulation of the PWL-Function-Based Chaotic Oscillators
	Cosimulation Between Active-HDL and Simulink
	Experimental Observation of Chaotic Attractors and Synchronization of Two Chaotic Oscillators
		Synchronization in a Master-Slave Topology
		Synchronization in a Master-Slave Topology for the Three Chaotic Oscillators
	Application to Image Transmission
	Conclusion
	References
16
On Nonidentical Discrete-Time Hyperchaotic Systems Synchronization: Towards Secure Medical Image Transmission
	Introduction
	Proposed Method for Coupled Nonidentical Chaotic Systems Synchronization Study
		Proposed Synchronization Method: Basic Idea
		Case of the Synchronization of Wang System Coupled to Hénon Hitzl Zele System
		Case of the Synchronization of Generalized Hénon 3D System Coupled to Stéfanski System
	Proposed Cryptosystem to Secure Medical Images Based on Coupled Hyperchaotic Hénon 3D and Stefanski Systems Synchroniz ...
		Cryptosystem Design: Problem Statement
		Encryption and Decryption Process and Results
		Measurement of Encryption and Decryption Quality
		Security Analysis
			Key Space Analysis
			Statistical Analysis
	Conclusion
	Appendix A [53]
	Appendix B [54]
	References
	Further Reading
17
Fractional-Order Hybrid Synchronization for Multiple Hyperchaotic Systems
	Introduction
	Preliminaries and Problem Position
		Preliminaries
		Problem Position
	Main Results
	Hybrid Synchronization Between Identical FO Hyperchaotic Systems
		FO Hyperchaotic Systems
		Control Design
		Simulation Results
	Hybrid Synchronization Between Nonidentical FO Hyperchaotic Systems
		Different FO Hyperchaotic Systems
		Control Design
		Simulation Results
	Conclusion
	References
	Further Reading
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	R
	S
	T
	V
	W
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