Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors

Abstract

This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with self-excited and hidden attractors. The book includes 20 chapters contributed by respected experts, which focus on various applications such as biological systems, memristor-based systems, fractional-order systems, finance systems, business cycles, oscillators, coupled systems, hyperchaotic systems, flexible robot manipulators, electronic circuits, and control models. Special attention is given to modeling, design, circuit realization, and practical applications to address recent research problems in nonlinear dynamical systems. The book provides a valuable reference guide to nonlinear dynamical systems for engineers, researchers, and graduate students, especially those whose work involves mechanics, electrical engineering, and control systems. 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.