Nonlinear Dynamics Integrability, Chaos and Patterns [Paperback]

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences who wish to gain a broad knowledge of nonlinear dynamics. It describes fundamental concepts, theoretical procedures, experimental and numerical techniques and technological applications of nonlinear dynamics. Numerous examples and problems are included to facilitate the understanding of the concepts and procedures described. In addition to 16 chapters of main material, the book contains 10 appendices which present in-depth mathematical formulations involved in the analysis of various nonlinear systems.1. What is Nonlinearity?.- 1.1 Dynamical Systems: Linear and Nonlinear Forces.- 1.2 Mathematical Implications of Nonlinearity.- 1.2.1 Linear and Nonlinear Systems.- 1.2.2 Linear Superposition Principle.- 1.3 Working Definition of Nonlinearity.- 1.4 Effects of Nonlinearity.- 2. Linear and Nonlinear Oscillators.- 2.1 Linear Oscillators and Predictability.- 2.1.1 Free Oscillations.- 2.1.2 Damped Oscillations.- 2.1.3 Damped and Forced Oscillations.- 2.2 Damped and Driven Nonlinear Oscillators.- 2.2.1 Free Oscillations.- 2.2.2 Damped Oscillations.- 2.2.3 Forced Oscillations  Primary Resonance and Jump Phenomenon (Hysteresis).- 2.2.4 Secondary Resonances (Subharmonic and Superharmonic).- 2.3 Nonlinear Oscillations and Bifurcations.- Problems.- 3. Qualitative Features.- 3.1 Autonomous and Nonautonomous Systems.- 3.2 Dynamical Systems as Coupled First-Order Differential lÃF