
Geometric Dynamical Systems: Manifolds and Stability Part I
04 May 2016   Contributor(s):: Christopher KRT Jones
This is the first part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a...

Geometric Dynamical Systems: Manifolds and Stability Part II
04 May 2016   Contributor(s):: Christopher KRT Jones
This is the second part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This is background lecture 3.1B for the Mathematics of Climate Modelling course.

Geometric Dynamical Systems: Manifolds and Stability Part III
04 May 2016   Contributor(s):: Christopher KRT Jones
This is the final part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This is background lecture 3.1C for the Mathematics of Climate Modelling course.

dBBCK: Chapter 2, part 2
30 Nov 2015   Contributor(s):: Kaitlin Hill
A discussion of the second part of of Chapter 2 in Piecewisesmooth Dynamical Systems by di Bernardo, Budd, Champneys, and Kowalczyk, which covers an introduction to piecewisesmooth ODEs, Filippov systems, and hybrid systems, as well as asymptotic stability of nonsmooth systems.

A nonsmooth example: An approximation to the Jormungand climate model
30 Nov 2015   Contributor(s):: Jim Walsh

Realistic modeling and analysis of synchronization dynamics in powergrid networks
08 May 2015   Contributor(s):: Takashi Nishikawa
An imperative condition for the functioning of a powergrid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. In this talk I will first give a comparative review of three leading...

Synchronization in power grid networks
07 May 2015   Contributor(s):: Suman Acharyya
This survey discusses Master Stability Function (MSF) analysis for determining stability of synchronization of coupled oscillators on network. In addition, we briefly discuss the derivation of the Swing equation that determine the dynamics of a node in power grid network, and...

Complex Energy Systems
07 May 2015   Contributor(s):: Michael Chertkov
This is the opening guest lecture for the Electric Grid Focus Group. Dr. Michael Chertkov of Los Alamos National Lab describes the statistical and mathematical problems arising in complex energy systems, including the electric grid and gas networks. Systems with high penetration of...

Computational Techniques for Lyapunov Exponents and Vectors
23 Mar 2015   Contributor(s):: Erik Van Vleck
In this talk we present computational techniques for Lyapunov exponents and vectors based upon continuous matrix factorizations (QR and SVD). We outline the techniques, their wellposedness, error analysis/perturbation theory, and describe codes we have developed. We then discuss application of...