Bibliothèque de L'IMIST/CNRST

From the Contents: Part I Dynamical Systems -- Stability of Dynamical Systems -- Linear Approach -- Bifurcations of Dynamical Systems -- Dynamical Systems With One Degree of Freedom -- Part II From Order to Chaos: Bifurcation Scenarios -- Robust and Nonrobust Dynamical Systems. Classification of Attractor Types -- Characteristics of Poincare Recurrences -- Fractals in Nonlinear Dynamics -- The Anishchenko–Astakhov Oscillator of Chaotic Self-Sustained Oscillations -- Quasiperiodic Oscillator with Two Independent Frequencies -- Synchronization of Periodic Self-Sustained Oscillations -- Synchronization of Two-Frequency Self-Sustained Oscillations.-Synchronization of Chaotic Oscillations -- References.

This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems.  This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.