Contents


Preface

This book examines some problems and current trends relating to the theory of dynamical systems. It also discusses some significant advances made in this field in the last several years, including new models, computer algorithms, and applications

The book includes six chapters. Chapter 1 presents an innovative methodology that integrates physical devices and machinery with text mining technologies to identify anomalous behaviors, even of minimal entity, rarely perceived by other strategies in a machine tool. Chapter 2 presents a vibrations analysis of elastic beams based on the constitutive equation of Kelvin-Voigt type, which contains fractional derivatives of real order. Chapter 3 discusses the emergence of chaos and complex behavior in real and physical systems, reviewing problems such as the complexity of Child's swing dynamics, chaotic neuronal dynamics, complex food-web dynamics, financial models, and others. Chapter 4 considers the invariant method theory for stochastic systems with strong perturbations, representing modern approaches to describe dynamical systems having a set of invariant functions. Chapter 5 presents a study of a mesoscopic stochastic process derived from deterministic dynamics studied by Kolmogorov and others in the stationary case, and extends their methods and some of their results considering the non-stationary process, which stems from a non-invariant initial measure. Finally, Chapter 6 introduces recent developments on the stability analysis of dynamical systems using the powerful tool of control

Researchers, engineers, and graduate students in both pure and applied mathematics may benefit from the chapters collected in this volume. We express appreciation to IntechOpen for their professional support and to Author Service Manager

Free University of Bozen-Bolzano (Faculty of Computer Science),

**Bruno Carpentieri**

Bolzano, Italy

Mr. Josip Knapić for his tireless help in the preparation of this book.

in various scientific areas.

Lyapunov functions.
