Preface
Organization
Executive Committee
Program Committee
Referees
Sponsoring Institutions
Contents
Part I Synchronization
1 Synchronization of Two Fiber Lasers with Optical Logarithmic Coupler: Experimental Implementation
1.1 Introduction
1.2 Dynamics of an Erbium-Doped Fiber Laser (EDFL)
1.2.1 Bifurcation Diagram and Periodic Attractors
1.2.2 Basin of Attraction
1.3 Experimental Setup and Bifurcation Diagrams
1.3.1 Experimental Setup
1.3.2 Optical Attenuator (OA)
1.3.3 Experimental Bifurcation Diagram of the Driver EDFL
1.3.4 Experimental Bifurcation Diagram of the Driven EDFL
1.4 Results
1.4.1 Bifurcation Diagrams of Laser Intensity of Driver and Driven EDFLs
1.4.2 Frequency Difference Between Driver and Driven EDFLs of Principal Component Domain of Fourier Transform
1.4.3 Synchronization Error Estimation
1.5 Conclusions
References
2 Anti-synchronization in a Pair of Coupled Multistable Systems
2.1 Introduction
2.2 System Model
2.2.1 Types of Coupling and Some Definition
2.3 Theoretical Analysis
2.4 Numerical Results
2.4.1 Complete Anti-synchronization
2.4.2 Partial Anti-synchronization
2.5 Conclusion
References
3 Analysis of Synchronizability in Small-World Complex Networks
3.1 Introduction
3.2 Complex Networks
3.2.1 Small-World Networks
3.2.2 Main Algorithms to Generate Small-World Complex Networks
3.2.3 SanchezโPosadas Algorithm
3.3 Chaotic Oscillators
3.3.1 Chua Chaotic Oscillator
3.4 Synchronization
3.4.1 Preliminaries of Small-World Network Synchronization
3.4.2 Eigenratio as a Synchronizability Measure
3.5 Results
3.6 Conclusions
References
Part II Cryptosystems
4 Generation of Dynamical S-Boxes via Lag Time Chaotic Series for Cryptosystems
4.1 Introduction
4.2 Criteria for a Good nn Bit S-Box
4.2.1 Bijective Criterion
4.2.2 Nonlinearity Criterion
4.2.3 Strict Avalanche Criterion (SAC)
4.2.4 Output Bits Independence Criterion (BIC)
4.2.5 Criterion of Equiprobable Input/Output XOR Distribution
4.2.6 Maximum Expected Linear Probability (MELP)
4.3 Analysis of the Logistic Map
4.4 Proposed Algorithm to Generate Dynamical S-Boxes
4.4.1 The Algorithm for S-Box Design via CSPRNG
4.5 Performance Test of S-Box
4.5.1 Bijectivity Criterion
4.5.2 Nonlinearity Criterion
4.5.3 Strict Avalanche Criterion (SAC)
4.5.4 Output Bits Independence Criterion (BIC)
4.5.5 Criterion of Equiprobable Input/Output XOR Distribution
4.5.6 MELP Criterion of the Generated S-Box
4.5.7 Comparative Results
4.6 Dynamical Generation of S-Boxes and Its Application
4.7 Concluding Remarks
References
5 Modification of the Quantum Logistic Map with Application in Pseudo-Random Bit Generation and Image Encryption
5.1 Introduction
5.2 The Quantum Logistic Map
5.3 Method for Achieving More Complex Chaotic Behavior
5.4 The Sine-Quantum Logistic Map
5.5 Pseudo-Random Bit Generation
5.6 Image Encryption Scheme
5.6.1 Outline of the Proposed Method
5.6.2 Determination of Shuffling/Encryption Key
5.6.3 Row/Column Shuffling Process
5.6.4 Image Splitting
5.6.5 Block Encryption/Decryption
5.6.6 Security Analysis of the Proposed Method
5.7 Conclusions
References
Part III Fractional Calculus
6 On the Relationship Between Integer and Fractional PWL Systems with Multistable Behavior
6.1 Introduction
6.2 Theory
6.2.1 Fractional Calculus
6.2.2 Multiscroll Chaotic System
6.3 Multistability in the PWL System Through Bifurcation Parameter
6.4 Multistability in the PWL System Through Derivative Order
6.5 Conclusions
References
7 Approximation of Fractional-Order Controllers for Mechatronic Applications
7.1 Introduction
7.2 Approximation Tools
7.3 Implementation Issues
7.4 Simulation Results
7.5 Conclusions
Appendix
References
Part IV Chaotic Systems
8 Comparative Analysis of Chaotic Features of Maps Without Fixed Points
8.1 Introduction
8.2 Unidimensional Maps
8.2.1 Logistic Map
8.2.2 Vertigo-2 Map
8.2.3 PWL Map
8.2.4 Bifurcation Diagrams
8.2.5 Lyapunov Exponents
8.2.6 Average Measurement to Sensitivity to Initial Conditions
8.2.7 Entropy Analysis
8.3 Bidimensional Maps
8.3.1 The Hรฉnon Map
Map Inspirited by Hรฉnon Map (IHM Map)
Quadratic Map
Map with No Fixed Points (NFP Map)
8.3.2 Time Series
8.3.3 Bifurcation Diagrams
8.3.4 Lyapunov Exponents Spectrum
8.3.5 Average Measurement to Sensitivity to Initial Conditions
8.3.6 Entropy of Bidimensional Maps
8.4 Conclusions
References
9 A New 4-D Hyperchaotic System with No Balance Point, Its Bifurcation Analysis, Multi-Stability, Circuit Simulation, and FPGA Realization
9.1 Introduction
9.2 A New 4-D Hyperchaotic System with No Balance Point
9.3 Bifurcation Analysis of the New 4-D Hyperchaotic System with No Balance Point
9.3.1 Bifurcation Analysis When a Varies
9.3.2 Bifurcation Analysis When b Varies
9.3.3 Bifurcation Analysis When c Varies
9.3.4 Coexistence of Attractors for the New 4-D Hyperchaotic System
9.4 MultiSim Electronic Circuit Design of the New 4-D Hyperchaotic System
9.5 FPGA Design of the New 4-D Hyperchaotic System with No Balance Point
9.6 Conclusion
References
10 Displacement of Equilibria and n-Double Wing Attractor Generation in the Piecewise Linearized Lorenz System
10.1 Introduction
10.2 Linearized Lorenz System
10.3 Displacement of the Equilibria of the Linearized Lorenz System
10.4 Curve Fitting for the n-Double Wing Attractor Generation
10.5 Conclusions
References
Part V Applications
11 Analysis of a Three-Dimensional Non-autonomous Chaotic Circuit with a Thermistor as a Physical Memristor
11.1 Introduction
11.2 The Proposed Nonlinear Circuit
11.3 Numerical Results
11.3.1 The Dynamics Related to the Capacitance C
11.3.2 The Dynamics Related to the Inductance L
11.3.3 The Dynamics Related to the Initial Conditions x0, y0, z0
11.4 Conclusion
References
12 Inverse Filter in the Growth of Urban Sprawl with Cellular Automata Model
12.1 Introduction
12.2 Material and Method
12.2.1 Cohen's Kappa Index
12.2.2 Jaccard Index
12.2.3 Fractal Dimension
12.2.4 Shannon Entropy
12.2.5 Inverse Filter
12.3 Results
12.4 Conclusions
References
13 A Metapopulation Network Model with Seasonal Succession to Analyze Dengue Disease in Mรฉxico
13.1 Introduction
13.2 Model Formulation
13.2.1 A Single Population Model
13.2.2 A Metapopulation Network Model
13.3 Numerical Example for Two Connected Patches
13.4 The Role of Climate Variables on Mosquito Egg Diapause: Open Problems and Perspectives
13.5 Conclusion
References
Index