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On Chaos and Anomalous Diffusion in Classical and Quantum Mechanical Systems

Description: The phenomenon of dynamically induced anomalous diffusion is both the classical and quantum kicked rotor is investigated in this dissertation. We discuss the capability of the quantum mechanical version of the system to reproduce for extended periods the corresponding classical chaotic behavior.
Date: August 1998
Creator: Stefancich, Marco
Partner: UNT Libraries

Fractional Calculus and Dynamic Approach to Complexity

Description: Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. Nonlinear Langevin equation describes the mean field of a finite size complex network at criticality. Critical phenomena and temporal complexity are two very important issues of modern nonlinear dynamics and the link between them found by the author can significantly improve the understanding behavior of dynamical systems at criticality. The subject of temporal complexity addresses the challenging and especially helpful in addressing fundamental physical science issues beyond the limits of reductionism.
Date: December 2015
Creator: Beig, Mirza Tanweer Ahmad
Partner: UNT Libraries

Synchronous Chaos, Chaotic Walks, and Characterization of Chaotic States by Lyapunov Spectra

Description: Four aspects of the dynamics of continuous-time dynamical systems are studied in this work. The relationship between the Lyapunov exponents of the original system and the Lyapunov exponents of induced Poincare maps is examined. The behavior of these Poincare maps as discriminators of chaos from noise is explored, and the possible Poissonian statistics generated at rarely visited surfaces are studied.
Date: August 1993
Creator: Albert, Gerald (Gerald Lachian)
Partner: UNT Libraries

Experimental Synchronization of Chaotic Attractors Using Control

Description: The focus of this thesis is to theoretically and experimentally investigate two new schemes of synchronizing chaotic attractors using chaotically operating diode resonators. The first method, called synchronization using control, is shown for the first time to experimentally synchronize dynamical systems. This method is an economical scheme which can be viably applied to low dimensional dynamical systems. The other, unidirectional coupling, is a straightforward means of synchronization which can be implemented in fast dynamical systems where timing is critical. Techniques developed in this work are of fundamental importance for future problems regarding high dimensional chaotic dynamical systems or arrays of mutually linked chaotically operating elements.
Date: December 1994
Creator: Newell, Timothy C. (Timothy Charles)
Partner: UNT Libraries