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Intro; Preface; Contents; Nonlinear Dynamical Systems with Self-Excited Attractors; 1 Bifurcation Analysis and Chaotic Behaviors of Fractional-Order Singular Biological Systems; Abstract; 1 Introduction; 2 Preliminary FOS Systems Theory; 2.1 Fractional-Order Systems; 2.2 FOS Systems; 3 Different Bifurcations and Chaos; 3.1 Saddle-Node Bifurcation; 3.2 Transcritical and Pitchfork Bifurcation; 3.3 Hopf Bifurcation; 3.4 Singularity Induced Bifurcation (SIB); 3.5 Chaotic Behavior; 4 Bifurcation Analysis and Chaotic Behaviors of FOS Biological Models; 4.1 Predator-Prey Models
4.1.1 Model Formulation and Qualitative Analysis4.1.2 Numerical Simulation; 4.2 Logistic Map; 4.2.1 Model Formulation; 4.2.2 Numerical Simulation; 4.3 SEIR Epidemic System; 4.3.1 Model Formulation; 4.3.2 Numerical Simulation; 5 Conclusions and Discussions; References; Chaos and Bifurcation in Controllable Jerk-Based Self-Excited Attractors; 1 Introduction; 2 Survey of the Related and Utilized Continuous and Discrete Chaotic Systems; 2.1 Jerk-Based Chaotic Attractors; 2.2 Two Modified Non-linearities; 3 Proposed Systems and Their Properties; 4 Simulation Results in Integer-Order Domain
4.1 Sensitivity to Main System Parameters4.2 Sensitivity to Scaling Parameters; 4.3 Co-existing and Multi-scroll Attractors; 5 Sensitivity to Fractional-Order Parameters; 6 Conclusions; References; Self-Excited Attractors in Jerk Systems: Overview and Numerical Investigation of Chaos Production; 1 Introduction; 2 Review of Some Self-Excited Jerk-Based Attractors; 3 Sensitivity to Parameter Variations; 3.1 A Dissipative Self-Excited Attractor with Quadratic Nonlinearity: System (6); 3.2 A Dissipative Self-Excited Attractor with Cubic Nonlinearity: System (8)
3.3 A Dissipative Self-Excited Attractor with Sinusoidal Nonlinearity: System (10)4 Conclusions; References; Synchronization Properties in Coupled Dry Friction Oscillators; 1 Introduction; 2 Synchronization; 2.1 Types of Synchronization; 2.2 Synchronous State Stability; 3 Single Self-excited Friction Oscillator; 4 Oscillators Network; 5 Results; 6 Conclusion; References; 5 Backstepping Control for Combined Function Projective Synchronization Among Fractional Order Chaotic Systems with Uncertainties and External Disturbances; Abstract; 1 Introduction; 2 Problem Formulation
3 Some Preliminaries, Definition and Lemma3.1 Fractional Calculus; 4 Systems' Description; 4.1 Fractional Order Lorenz System; 4.2 Fractional Order Rossler Systems; 4.3 Fractional Order Chen System; 5 Combined Function Projective Synchronization Among Fractional Order Chaotic Systems with Uncertainties and External Disturbances Using Backstepping Control Method; 5.1 Numerical Simulation and Results; 6 Conclusion; References; Chaotic Business Cycles within a Kaldor-Kalecki Framework; 1 Introduction; 2 Literature Review; 2.1 On the Business Cycles; 2.2 On the Recurrence Quantification Analysis
4.1.1 Model Formulation and Qualitative Analysis4.1.2 Numerical Simulation; 4.2 Logistic Map; 4.2.1 Model Formulation; 4.2.2 Numerical Simulation; 4.3 SEIR Epidemic System; 4.3.1 Model Formulation; 4.3.2 Numerical Simulation; 5 Conclusions and Discussions; References; Chaos and Bifurcation in Controllable Jerk-Based Self-Excited Attractors; 1 Introduction; 2 Survey of the Related and Utilized Continuous and Discrete Chaotic Systems; 2.1 Jerk-Based Chaotic Attractors; 2.2 Two Modified Non-linearities; 3 Proposed Systems and Their Properties; 4 Simulation Results in Integer-Order Domain
4.1 Sensitivity to Main System Parameters4.2 Sensitivity to Scaling Parameters; 4.3 Co-existing and Multi-scroll Attractors; 5 Sensitivity to Fractional-Order Parameters; 6 Conclusions; References; Self-Excited Attractors in Jerk Systems: Overview and Numerical Investigation of Chaos Production; 1 Introduction; 2 Review of Some Self-Excited Jerk-Based Attractors; 3 Sensitivity to Parameter Variations; 3.1 A Dissipative Self-Excited Attractor with Quadratic Nonlinearity: System (6); 3.2 A Dissipative Self-Excited Attractor with Cubic Nonlinearity: System (8)
3.3 A Dissipative Self-Excited Attractor with Sinusoidal Nonlinearity: System (10)4 Conclusions; References; Synchronization Properties in Coupled Dry Friction Oscillators; 1 Introduction; 2 Synchronization; 2.1 Types of Synchronization; 2.2 Synchronous State Stability; 3 Single Self-excited Friction Oscillator; 4 Oscillators Network; 5 Results; 6 Conclusion; References; 5 Backstepping Control for Combined Function Projective Synchronization Among Fractional Order Chaotic Systems with Uncertainties and External Disturbances; Abstract; 1 Introduction; 2 Problem Formulation
3 Some Preliminaries, Definition and Lemma3.1 Fractional Calculus; 4 Systems' Description; 4.1 Fractional Order Lorenz System; 4.2 Fractional Order Rossler Systems; 4.3 Fractional Order Chen System; 5 Combined Function Projective Synchronization Among Fractional Order Chaotic Systems with Uncertainties and External Disturbances Using Backstepping Control Method; 5.1 Numerical Simulation and Results; 6 Conclusion; References; Chaotic Business Cycles within a Kaldor-Kalecki Framework; 1 Introduction; 2 Literature Review; 2.1 On the Business Cycles; 2.2 On the Recurrence Quantification Analysis