Nekorkin V.I. Introduction to Nonlinear Oscillations

Wiley-VCH, 2015. — ISBN: 978-3-527-41330-0.A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.Introduction to the Theory of Oscillations
One-Dimensional Dynamics
Stability of Equilibria. A Classification of Equilibria of Two-Dimensional Linear Systems
Analysis of the Stability of Equilibria of Multidimensional Nonlinear Systems
Linear and Nonlinear Oscillators
Basic Properties of Maps
Limit Cycles
Basic Bifurcations of Equilibria in the Plane
Bifurcations of Limit Cycles. Saddle Homoclinic Bifurcation
The Saddle-Node Homoclinic Bifurcation. Dynamics of Slow–Fast Systems in the Plane
Dynamics of a Superconducting Josephson Junction
The Van der Pol Method. Self-Sustained Oscillations and Truncated Systems
Forced Oscillations of a Linear Oscillator
Forced Oscillations in Weakly Nonlinear Systems with One Degree of Freedom
Forced Synchronization of a Self-Oscillatory System with a Periodic External Force
Parametric Oscillations
Answers to Selected Exercises