arXiv subjects

James Yorke

Publications and source records attributed to James Yorke.

3 recordsLinked to original sources

arXiv2016

Indestructible dynamics of torus maps

Given a $d$-dimensional torus map $F(z)=Mz+G(z)\bmod 1$, where $M$ is an integer-matrix and and $G$ is a periodic function, we find conditions on $M$ under which $F$ is semi-conjugate to a linear torus map, independently of $G$. We also find a conditions $G$ under which these semi-conjugacies can be turned into conjugacies. These conditions are satisfied by open sets of torus maps (in the $C^1$-topology) and therefore describe some asymptotic behavior of trajectories which are stable under perturbations to the map.

math.DS↗

arXiv2015

Avoiding extremes using Partial Control

Dynamical systems can be prone to severe fluctuations due to the presence of chaotic dynamics. This paper explains for a toy chaotic economic model how such a system can be regulated by the application of relatively weak control to keep the system confined to a bounded region of the phase space, even in the presence of strong external disturbances. Since the control here is weaker than the disturbance, the system cannot be controlled to a particular trajectory, but under certain circumstances it can be partially controlled to avoid extreme values. Partial control depends on the existence of a certain set called a "safe sets". We describe the safe set and how it varies with parameters, sometimes continuously and sometimes discontinuously.

math.DS↗

arXiv2004

Two Models for the Study of Congested Internet Connections

In this paper, we introduce two deterministic models aimed at capturing the dynamics of congested Internet connections. The first model is a continuous-time model that combines a system of differential equations with a sudden change in one of the state variables. The second model is a discrete-time model with a time step that arises naturally from the system. Results from these models show good agreement with the well-known ns network simulator, better than the results of a previous, similar model. This is due in large part to the use of the sudden change to reflect the impact of lost data packets. We also discuss the potential use of this model in network traffic state estimation.

cs.NI↗