Μελέτη της δυναμικής συμπεριφοράς συζευγμένων μη-γραμμικών ταλαντώσεων
Creators: name: Βόλος, Χρήστος Κ.
Publisher: name: Aristotle University of Thessaloniki
Year: 2008
Subjects: Συγχρονισμός
Κρυπτογραφία
Ελεγχος δυναμικής συμπεριφοράς
Γεννήτρια παραγωγής τυχαίων αριθμών
Sychronization
Cryptography
Control of the dunamic behavior
Random number generator

description: Στην παρούσα διδακτορική διατριβή μελετήθηκε το φαινόμενο του συγχρονισμού μέσω της σύζευξης μη-γραμμικών ηλεκτρονικών κυκλωμάτων. Για το σκοπό αυτό χρησιμοποιήθηκαν δυο διαφορετικά κυκλώματα και πραγματοποιήθηκε η σύζευξη με δύο τρόπους, τη γραμμική σύζευξη και με τη μέθοδο του αντίστροφου συστήματος. Επίσης μελετήθηκε η εφαρμογή αυτών των κυκλωμάτων σε ένα αναλογικό κρυπτογραφικό σύστημα καθώς και σε μια γεννήτρια παραγωγής τυχαίων BITS
description: This PhD Thesis was done in the Physics Department of the Aristotle University of Thessaloniki. The subject of this work was the study of dynamics of two coupled nonlinear electronic circuits, the achievement of chaotic synchronization and the possible applications of this phenomenon. This thesis consists of eleven chapters, divided in three sections. In the first section, which includes the first four chapters, the theoretical analysis of nonlinear dynamics and chaos theory, along with synchronization and control phenomena are studied. In particular, in the first chapter a theoretical description of the system and especially of the dynamical system is presented. Basic concepts of nonlinear dynamics such as attractors, stability of the equilibria points, and phase portraits are referred. Methods of analyzing systemΆs chaotic behavior such as Lyapunov exponents, dimensions of the system, Poincaré maps and power spectra are described. In the second chapter, a theoretical analysis of a nonautonomous system, which is described by a DuffingΆs equation, is given. This nonlinear dynamical system is also used in the case of the linear coupling of the identical systems, which is done in chapter three. Also, in the fourth chapter, control of the chaotic behavior of the DuffingΆs system via a linear coupling with an identical system, which is in periodic state, is studied. The second section includes chapters five to eight and contains the experimental results. In particular, in the fifth chapter the study and implementation of a nonlinear electronic circuit, which is described by a DuffingΆs equation, is done. In the next chapter, the experimental coupling between two identical DuffingΆs type circuits via a linear resistor RC is implemented and chaotic synchronization is observed. In chapter seven, the case of chaotic synchronization of two DuffingΆs circuits with the inverse system approach is theoretically and experimentally studied. Chapter eight includes the results of the inverse system approach in a chaotic cryptographic scheme. The third section consists of the three last chapters and deals with the circuit which produces double scroll chaotic attractors. This circuit is studied theoretically and experimentally in chapter nine. In chapter ten, the results of the experimental coupling between two identical double scroll circuits via a linear resistor RC, is described. Finally, in last chapter, one more application of chaotic circuits is mentioned. The double scroll circuit, which is implemented, is used theoretically as a true random bit generator