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E-raamat: Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications

Edited by (Amirkabir University of Technology, Iran), Edited by (Full Professor, National Institute of Applied Sciences and Technology (INSAT), University of Carthage, Tunisia)
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Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications is a major reference for scientists and engineers interested in applying new computational and mathematical tools for solving complex problems related to modeling, analyzing and synchronizing chaotic systems. Furthermore, it offers an array of new, real-world applications in the field. Written by eminent scientists in the field of control theory and nonlinear systems from 19 countries (Cameroon, China, Ethiopia, France, Greece, India, Italia, Iran, Japan, Mexico, and more), this book covers the latest advances in chaos theory, along with the efficiency of novel synchronization approaches.

Readers will find the fundamentals and algorithms related to the analysis and synchronization of chaotic systems, along with key applications, including electronic design, text and image encryption, and robot control and tracking.

  • Explores and evaluates the latest real-world applications of chaos across various engineering and biomedical engineering fields
  • Investigates advances in chaos synchronization techniques, including the continuous sliding-mode control approach, hybrid synchronization between chaotic and hyperchaotic systems, and neural network synchronization
  • Presents recent advances in chaotic systems through an overview of new systems and new proprieties
Contributors xiii
Preface xvii
Part I New Chaotic Systems: Design and Analysis
1 Experimental Observations and Circuit Realization of a Jerk Chaotic System With Piecewise Nonlinear Function
3(20)
Abir Lassoued
Olfa Boubaker
Rachid Dhifaoui
Sajad Safari
1 Introduction
3(1)
2 Mathematical Model and Basic Properties
4(1)
3 Dynamic Analysis
5(8)
3.1 Equilibrium and Stability
5(5)
3.2 Routes to Chaos
10(1)
3.3 Lyapunov Exponents Analysis
11(1)
3.4 Comparative Analysis
12(1)
4 Circuit Design
13(4)
5 Experimental Results
17(1)
6 Conclusion
18(2)
References
20(3)
2 Analytical, Numerical and Experimental Analysis of an RC Autonomous Circuit With Diodes in Antiparallel
23(18)
Sifeu Takougang Kingni
Bonaventure Nana
Guy R. Kol
Victor Kamdoum Jamba
Paul Woafo
1 Introduction
23(2)
2 Analysis of Autonomous RC Circuit With Diodes in Antiparallel
25(11)
2.1 Symmetry, Invariance, Dissipative Character, and Linear Stability of the Equilibrium Points
26(3)
2.2 Dynamical Behaviors of the Circuit
29(6)
2.3 Observation of Chaotic Attractors From the Oscilloscope
35(1)
3 Conclusion
36(1)
Acknowledgment
37(1)
References
37(4)
3 Chaos in a System With Parabolic Equilibrium
41(22)
Viet-Thanh Pham
Christos K. Volos
Sundarapandian Vaidyanathan
Sajad Jafari
Cokul P.M.
Tomasz Kapitaniak
1 Introduction
41(2)
2 Model of a System With Infinite Equilibria
43(1)
3 Dynamical Properties of the System With Parabolic Equilibrium
44(1)
3.1 Equilibrium Points and Stability
44(1)
3.2 Dynamical Behavior
45(1)
4 Circuitry Implementation of the System With Parabolic Equilibrium
45(3)
5 Adaptive Control of the System With Parabolic Equilibrium
48(4)
6 Adaptive Synchronization of Two Systems With Parabolic Equilibrium
52(3)
7 Discussion
55(3)
8 Conclusion
58(1)
Acknowledgments
58(1)
References
58(5)
4 A New Four-Dimensional Chaotic System With No Equilibrium Point
63(14)
Shirin Panahi
Viet-Thanh Pham
Karthikeyan Rajagopal
Olfa Boubaker
Sajad Jafari
1 Introduction
63(1)
2 New No Equilibrium Chaotic System
64(1)
3 Fractional Order Hyperjerk System (FOHJS)
65(5)
3.1 Bifurcation
68(2)
4 Circuit Design
70(2)
5 Conclusion
72(1)
References
72(5)
5 A New Five Dimensional Multistable Chaotic System With Hidden Attractors
77(12)
Atefeh Ahmadi
Karthikeyan Rajagopal
Viet-Thanh Pham
Olfa Boubaker
Sajad Jafari
1 Introduction
77(1)
2 New System and Its Dynamical Properties
78(1)
3 Digital Implementation for the System Using Field Programmable Gate Arrays
78(4)
4 Analog Circuit Design
82(2)
5 Conclusion
84(1)
Acknowledgment
84(1)
References
84(5)
6 Extreme Multistability in a Hyperjerk Memristive System With Hidden Attractors
89(16)
Dimitrios A. Prousalis
Christos K. Volos
Bocheng Bao
Efthymia Meletlidou
Ioannis N. Stouboulos
Ioannis M. Kyprianidis
1 Introduction
89(2)
2 The Hyperjerk Memristive System
91(5)
3 System's Extreme Multistability
96(5)
4 Conclusion
101(1)
References
101(2)
Further Reading
103(2)
7 Parameter Estimation of Chaotic Systems Using Density Estimation of Strange Attractors in the State Space
105(22)
Vasser Shekofteh
Shirin Panahi
Olfa Boubaker
Sajad Jafari
1 Introduction
105(1)
2 A New Chaotic System and Its Bifurcation Analysis
106(1)
3 Density Estimation of the Attractor in the State Space Using GMM
107(5)
3.1 Initialization Step
109(1)
3.2 Expectation Step
110(1)
3.3 Maximization Step
110(1)
3.4 Likelihood Score Evaluation
110(1)
3.5 Determining the Appropriate Number of Gaussian Components
111(1)
4 Parameter Estimation of the Chaotic System Using GMM-Based Cost Functions
112(1)
4.1 Learning Phase
112(1)
4.2 Evaluation Phase
112(1)
5 Simulation Results
113(9)
5.1 The GMM of the Chaotic System
113(2)
5.2 1D Parameter Estimation of the Chaotic System
115(1)
5.3 The Effect of the Length of the Evaluation Data
116(4)
5.4 2D Parameter Estimation of the Chaotic System
120(2)
6 Conclusion
122(1)
Acknowledgment
123(1)
References
123(4)
Part II Real World Applications
8 Virtualization of Chua's Circuit State Space
127(38)
Branislav Sobota
Milan Cuzan
1 Introduction
127(1)
2 Chua's Circuit
128(1)
3 Boundary Surface
129(1)
4 Virtual Reality and Other Visualization Forms
130(5)
4.1 3D Virtualization Sequence and Its Implementation
130(1)
4.2 Input Data Preparation and Acquisition
131(1)
4.3 Modeling, Editing and Verification
131(1)
4.4 Visualization and Working With Virtual World
132(1)
4.5 3D Display Systems
133(1)
4.6 3D Printing and Real Objects Creation
134(1)
5 Visualization and Immersive Environments
135(2)
5.1 Mixed Reality System Implementation
136(1)
5.2 CAVE System Implementation
137(1)
6 Visualization of Objects in State Space
137(14)
6.1 Visualization of a Chaotic Attractor by Software Means
138(7)
6.2 Visualization of BS
145(6)
6.3 Visualization in Virtual Cave Environment
151(1)
7 Possibilities of Calculation of C-SBS
151(8)
7.1 Calculation of C-SBS by a PC With Single or Multicore Processor
154(5)
7.2 GRID Technology or High-Performance Computer Clusters
159(1)
7.3 GPGPU Technology Usage
159(1)
8 Conclusion
159(1)
References
160(5)
9 Some New Chaotic Maps With Application in Stochastic
165(22)
Ezzedine Mliki
Navid Hasanzadeh
Fahimeh Nazarimehr
Akif Akgul
Olfa Boubaker
Sajad Jafari
1 Introduction
165(1)
2 One-dimensional White Gaussian Noise Generator
166(9)
3 Attention Deficit Disorder Model
175(6)
4 Discussion and Conclusion
181(1)
References
182(5)
10 Chaotic Solutions in a Forced Two-Dimensional Hindmarsh-Rose Neuron
187(24)
Zahra Rostami
Mohsen Mousavi
Karthikeyan Rajagopal
Olfa Boubaker
Sajad Jafari
1 Introduction
187(3)
2 Model and Description
190(1)
3 Numerical Results of the Bifurcation Analysis
191(3)
4 Numerical Results of Wave Propagation in the Designed Network
194(12)
5 Conclusion
206(1)
References
207(4)
11 PD Bifurcation and Chaos Behavior in a Predator-Prey Model With Allee Effect and Seasonal Perturbation
211(22)
Afef Ben Saad
Olfa Boubaker
Zeraoulia Elhadj
1 Introduction
211(1)
2 Mathematical Modeling
212(1)
3 Preliminaries
213(1)
4 Dynamical Analysis of System for Both Types of Allee Effect
213(4)
5 Numerical Analysis
217(13)
5.1 Predator-Prey System With Strong Allee Effect
217(4)
5.2 Predator-Prey System With Weak Allee Effect Case Study
221(6)
5.3 Seasonally Perturbed System
227(3)
6 Conclusion
230(1)
References
231(2)
12 Chaotic Path Planning for a Two-Link Flexible Robot Manipulator Using a Composite Control Technique
233(28)
Kshetrimayum Lochan
Jay Prakash Singh
Binoy Krishna Roy
Bidyadhar Subudhi
1 Introduction
233(3)
2 Modeling of the Two-Link Flexible Manipulator
236(3)
3 Singular Perturbation Modeling of a TLFM
239(2)
3.1 Dynamic Model of the Slow Subsystem
240(1)
3.2 Dynamic Model of the Fast Subsystem
240(1)
4 Design of a Composite Control
241(3)
4.1 Dynamic Surface Control of the Slow Subsystem
241(1)
4.2 Backstepping Control for the Fast Subsystem
242(2)
5 Chaotic Signal as the Desired Trajectory
244(1)
6 Results and Discussion for the Composite Control
244(8)
6.1 Simulation Results With the Nominal Payload (0.145 kg)
245(3)
6.2 Chaotic Trajectory Tracking With a 0.3 kg Payload
248(4)
7 Conclusions
252(1)
References
252(9)
Part III New Trends in Chaos Synchronization
13 Robust Synchronization of Master Slave Chaotic Systems: A Continuous Sliding-Mode Control Approach With Experimental Study
261(16)
Hafiz Ahmed
Hector Rios
Ivan Salgado
1 Introduction
261(2)
2 Preliminaries
263(1)
3 Problem Statement
263(1)
4 Output-Feedback-Based Continuous Singular Terminal Sliding-Mode (CSTSM) Controller Design
264(3)
4.1 Finite-Time Sliding-Mode Observer
266(1)
5 Numerical Simulation Results
267(3)
6 Experimental Study
270(2)
7 Conclusion
272(1)
References
273(4)
14 A Four-Dimensional Chaotic System With One or Without Equilibrium Points: Dynamical Analysis and Its Application to Text Encryption
277(24)
Victor Kamdoum Jamba
Romanic Kengne
Sifeu Takougang Kingni
Hilaire Bertrand Fotsin
1 Introduction
277(2)
2 Model of Proposed Autonomous System With One or Without Equilibrium Points
279(1)
3 Dynamical Analysis of Proposed Autonomous System With One or Without Equilibrium Points
280(7)
3.1 Self-Excited Attractor in Proposed Autonomous System With Only One Equilibrium Point
280(1)
3.2 Hidden Attractor in Proposed Autonomous System Without Equilibrium Point
281(6)
4 Electronic Circuit Implementation of Proposed Autonomous System With One or Without Equilibrium Points
287(4)
5 Adaptive Finite-Time Synchronization of Proposed Autonomous System With Hidden Attractor
291(5)
5.1 Preliminaries
292(1)
5.2 Main Results
293(2)
5.3 Numerical Verifications
295(1)
6 A Text Encryption Application Using Hidden Chaotic Attractor of Proposed Autonomous System With One or Without Equilibrium Points
296(2)
6.1 Proposed Affine Cipher
296(1)
6.2 Key Generation
296(1)
6.3 Numerical Verifications
297(1)
7 Concluding Remarks
298(1)
References
299(2)
15 FPGA Implementation of Chaotic Oscillators, Their Synchronization, and Application to Secure Communications
301(28)
Esteban Tlelo-Cuautle
Omar Guillen-Fernandez
Jose de Jesus Rangel-Magdaleno
Ashley Melendez-Cano
Jose Cruz Nunez-Perez
Luis Gerardo de la Fraga
1 Introduction
301(2)
2 Simulation of Chaotic Oscillators Based on PVVL Functions
303(3)
2.1 Numerical Methods to Simulate Chaotic Oscillators
305(1)
2.2 Simulation of the PWL-Function-Based Chaotic Oscillators
306(1)
3 Cosimulation Between Active-HDL and Simulink
306(5)
4 Experimental Observation of Chaotic Attractors and Synchronization of Two Chaotic Oscillators
311(8)
4.1 Synchronization in a Master-Slave Topology
316(3)
4.2 Synchronization in a Master-Slave Topology for the Three Chaotic Oscillators
319(4)
5 Application to Image Transmission
323(3)
6 Conclusion
326(1)
Acknowledgments
326(1)
References
326(3)
16 On Nonidentical Discrete-Time Hyperchaotic Systems Synchronization: Towards Secure Medical Image Transmission
329(22)
Narjes Khalifa
Mohamed Benrejeb
1 Introduction
329(2)
2 Proposed Method for Coupled Nonidentical Chaotic Systems Synchronization Study
331(6)
2.1 Proposed Synchronization Method: Basic Idea
331(2)
2.2 Case of the Synchronization of Wang System Coupled to Henon Hitzl Zele System
333(3)
2.3 Case of the Synchronization of Generalized Henon 3D System Coupled to Stefanski System
336(1)
3 Proposed Cryptosystem to Secure Medical Images Based on Coupled Hyperchaotic Henon 3D and Stefanski Systems Synchronization
337(8)
3.1 Cryptosystem Design: Problem Statement
337(2)
3.2 Encryption and Decryption Process and Results
339(2)
3.3 Measurement of Encryption and Decryption Quality
341(1)
3.4 Security Analysis
341(4)
4 Conclusion
345(1)
Appendix A
345(1)
Appendix B
346(1)
References
346(3)
Further Reading
349(2)
17 Fractional-Order Hybrid Synchronization for Multiple Hyperchaotic Systems
351(16)
Abir Lassoued
Olfa Boubaker
1 Introduction
351(1)
2 Preliminaries and Problem Position
352(2)
2.1 Preliminaries
352(1)
2.2 Problem Position
353(1)
3 Main Results
354(2)
4 Hybrid Synchronization Between Identical FO Hyperchaotic Systems
356(4)
4.1 FO Hyperchaotic Systems
356(1)
4.2 Control Design
357(1)
4.3 Simulation Results
358(2)
5 Hybrid Synchronization Between Nonidentical FO Hyperchaotic Systems
360(3)
5.1 Different FO Hyperchaotic Systems
360(1)
5.2 Control Design
361(2)
5.3 Simulation Results
363(1)
6 Conclusion
363(2)
References
365(1)
Further Reading
366(1)
Index 367
Pr. Olfa Boubaker is a full professor at the National Institute of Applied Sciences and Technology (INSAT) at the University of Carthage, Tunisia, where she specializes in control theory, nonlinear systems, and robotics. She holds a Ph.D. in Electrical Engineering from the National Engineering School of Tunis and a Habilitation Universitaire in Control Engineering from the National Engineering School of Sfax. Professor Boubaker has led numerous research projects in sustainable development, including medical robotics and green energy. She has authored over 150 peer-reviewed papers and several books, and she is the founder/editor of the book series Medical Robots and Devices. Additionally, she serves as an associate editor for the journal Robotica and the International Journal of Advanced Robotic Systems, contributing to various scientific journals and mentoring numerous engineering graduates. Sajad Jafari was born in Kermanshah, Iran, in 1983. He received his BSc., M.S., and Ph.D. degrees in biomedical engineering in 2005, 2008, 2013 from biomedical engineering department, Amirkabir University of technology, Tehran, Iran. He is currently an Assistant Professor in there (since 2013). His research interests include artificial intelligence, optimization, pattern recognition and especially nonlinear and chaotic signals and systems. Dr Sajad Jafari is closely associated with several reputable international journals as a reviewer and he is the author/coauthor of more than 100 peer-reviewed papers.