Introduction to Nonlinear Dynamic Systems (ebook)

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Author Biography
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The ebook is available for free to students and non-students, through the institution's official website:
| Kallipos.gr |

This book is an introduction to the study of Non-Linear Systems and is aimed at 3rd-4th year undergraduate students of Science or Engineering. It could also be used as a basis in a corresponding course of a Master's Degree Program.

The aim of the book is for the student to understand the basic methods we use in dynamical systems, their limits, the concept of stability and what are the necessary conditions for complex behavior to occur. Because the analytical mathematical approach of a dynamical system in general is difficult for an undergraduate student, we focus on computational techniques. We use Mathematica (or the free Mathics software) which easily combines analytical and numerical calculations as well as graphics.

The book initially deals with simple mechanical systems and more generally autonomous continuous systems in two dimensions. The basic points of dynamics are described in detail such as equilibrium points, stability, characteristics of the topology of the phase space, bifurcations, periodic solutions and limit cycles. These characteristics are described, mainly computationally, and for three-dimensional systems. For non-autonomous systems, we stay in one dimension and oscillator systems with an external periodic perturbation. Possible cases of behavior (periodic or semi-periodic oscillations, limit cycles, chaotic behavior) are described.
The second part of the book deals with discrete one- and two-dimensional systems. We study their fixed and periodic points as well as their linear stability. Through classical systems (such as logistic representation) we show the transition from order to chaos and give the property of chaos with a rigorous mathematical definition. At the end we present the illustration of Smale's horseshoe and the creation of the homoclinic mesh in preserved illustrations.

* The ebook was developed in the context of of the "Kallipos - Greek Academic Electronic Books & Aids" program, which took place with the participation of HEALLINK (Association of Greek Academic Libraries), grnet (National Research & Technology Network), National Technical University of Athens and the European Union, while it was co-financed by Greece (Ministry of Education & Religious Affairs, Special Management Service) and the European Union (NSRF 2007-2013, European Community Fund).

The selection of the writing effort coefficient for the design & development of each ebook was made by the respective author - academic - university professor, while our artistic director at the time, Nikolaos Koumartzis, participated in the registers of the "Kallipos" program.

The ebook is available for free to students and non-students, through the institution's official website:
| Kallipos.gr |

Author Biography

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