Dynamical Systems Commons^™

Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers

HMC Senior Theses

The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and …

Noise, Delays, And Resonance In A Neural Network, Austin Quan

HMC Senior Theses

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential …

A Stochastic Model For Wind Turbine Power Quality Using A Levy Index Analysis Of Wind Velocity Data, Jonathan Blackledge, Eugene Coyle, Derek Kearney

Conference papers

The power quality of a wind turbine is determined by many factors but time-dependent variation in the wind velocity are arguably the most important. After a brief review of the statistics of typical wind speed data, a non- Gaussian model for the wind velocity is introduced that is based on a Levy distribution. It is shown how this distribution can be used to derive a stochastic fractional diusion equation for the wind velocity as a function of time whose solution is characterised by the Levy index. A Levy index numerical analysis is then performed on wind velocity data for both …

Neutrosophic Interval Bialgebraic Structures, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors for the first time introduce the notion of neutrosophic intervals and study the algebraic structures using them. Concepts like groups and fields using neutrosophic intervals are not possible. Pure neutrosophic intervals and mixed neutrosophic intervals are introduced and by the very structure of the interval one can understand the category to which it belongs. We in this book introduce the notion of pure (mixed) neutrosophic interval bisemigroups or neutrosophic biinterval semigroups. We derive results pertaining to them. The new notion of quasi bisubsemigroups and ideals are introduced. Smarandache interval neutrosophic bisemigroups are also introduced and …

On The (Non)-Integrability Of Kdv Hierarchy With Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov

Articles

Nonholonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called “squared solutions” (squared eigenfunctions). Such deformations are equivalent to a perturbed model with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV6 equation are analysed. This allows for a formulation of conditions on the perturbation terms that preserve its integrability. The perturbation corrections to the scattering data and to the corresponding action-angle (canonical) variables are studied. The analysis shows …

Differential Geometry Of Moving Surfaces And Its Relation To Solitons, Andrei Ludu

Publications

In this article we present an introduction in the geometrical theory of motion of curves and surfaces in R 3 , and its relations with the nonlinear integrable systems. The working frame is the Cartan’s theory of moving frames together with Cartan connection. The formalism for the motion of curves is constructed in the Serret-Frenet frames as elements of the bundle of adapted frames. The motion of surfaces is investigated in the Gauss-Weingarten frame. We present the relations between types of motions and nonlinear equations and their soliton solutions.

Inverse Scattering Transform For The Degasperis–Procesi Equation, Adrian Constantin, Rossen Ivanov, Jonatan Lenells

Articles

We develop the Inverse Scattering Transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method are presented.

Reconstructability Analysis Of Elementary Cellular Automata, Martin Zwick, Hui Shi

Systems Science Friday Noon Seminar Series

Reconstructability analysis is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss (reduction in constraint) into lower ordinality relations. Set-theoretic reconstructability analysis (SRA) is used to characterize the mappings of elementary cellular automata. The degree of lossless decomposition possible for each mapping is more effective than the λ parameter (Walker & Ashby, Langton) as a predictor of chaotic dynamics.

Complete SRA yields not only the simplest lossless structure but also a vector of losses of all decomposed structures, indexed by parameter, τ. This vector subsumes λ, Wuensche’s Z parameter, and Walker …

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …

Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher

Theses and Dissertations

This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …

Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, Matthew Samuel Rothlisberger

CMC Senior Theses

Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.