2,754 research outputs found
Transient spatiotemporal chaos on complex networks
Thesis (M.S.) University of Alaska Fairbanks, 2004Some of today's most important questions regard complex dynamical systems with many interacting components. Network models provide a means to gain insight into such systems. This thesis focuses on a network model based upon the Gray-Scott cubic autocatalytic reaction-diffusion system that manifests transient spatiotemporal chaos. Motivated by recent studies on the small-world topology discovered by Watts and Strogatz, the network's original regular ring topology was modified by the addition of a few irregular connections. The effects of these added connections on the system's transience as well on the dynamics local to the added connections were examined. It was found that the addition of a single connection can significantly effect the transient time of spatiotemporal chaos and that the addition of two connections can transform the system's spatiotemporal chaos from transient to asymptotic. These findings suggest that small modifications to a network's topology can greatly affect its behavior.Introduction -- Background -- Transient spatiotemporal chaos in the presence of one shortcut -- Local dynamics in the vicinity of a shortcut -- Conclusion -- Bibliography
The minimum and maximum number of rational points on jacobian surfaces over finite fields
We give some bounds on the numbers of rational points on abelian varieties
and jacobians varieties over finite fields. The main result is that we
determine the maximum and minimum number of rational points on jacobians
varieties of dimension 2
Codes from Jacobian surfaces
This paper is concerned with some Algebraic Geometry codes on Jacobians of
genus 2 curves. We derive a lower bound for the minimum distance of these codes
from an upper "Weil type" bound for the number of rational points on
irreducible (possibly singular or non-absolutely irreducible) curves lying on
an abelian surface over a finite field
The characteristic polynomials of abelian varieties of dimensions 3 over finite fields
We describe the set of characteristic polynomials of abelian varieties of
dimension 3 over finite fields
The characteristic polynomials of abelian varieties of dimensions 4 over finite fields
We describe the set of characteristic polynomials of abelian varieties of
dimension 4 over finite fields
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