For recent publications please see this Google Scholar link. Publications related to data assimilation are also on the UMD Weather & Chaos publication page.

Below is mainly an index through 2005 to my journal articles, and a few papers from conference proceedings, organized into several themes. In most cases, the last line of a reference is a link to a journal web site with the abstract (and link to full text) for the paper, or in some cases a link straight the full text. Access to the full text requires a subscription for some journals. For a few papers, the title is a link to a preprint version. For others, you may be able to find preprint versions via Google Scholar.


Weather Forecasting and State Estimation for Spatiotemporal Chaos

These papers discuss mathematical applications to weather forecasting models and other high-dimensionals dynamical systems. Many are concerned with the problem of state estimation: determining the most likely state of a system, given a model for the system and limited observations made over a period of time. Click here for preprints and related publications.

Prevalence, Projection, and Dimension

These papers develop and apply the notion of "prevalence" to describe what is measure-theoretically typical in a space Some applications are to dynamics, and others are to describe the effect that a typical "projection" has on a set or a measure in a vector space, where by projection I mean a smooth (not necessarily linear) mapping into a lower dimensional space.

Fractals and Dimension in Dynamical Systems

These papers consider fractal sets and measures that arise in dynamical systems, and their characterization by various notions of "dimension". Some of the papers in Prevalence also discuss properties of fractal dimensions.

Optimal Orbits and Invariant Measures of Chaotic Systems

These papers involve invariant measures of chaotic dynamical systems. Several of them develop and study the question of which orbit or invariant measure of a chaotic system is "optimal", in the sense that it maximizes the average of some real-valued function of the system state.

Dynamics on Networks

These papers consider models of network growth, the dynamics of networks of coupled oscillators, and the dynamics of TCP networks.

Dynamics near Invariant Manifolds: Intermingled Basins, Bubbling, and Synchronization

These papers are concerned with the dynamics of systems with a invariant manifold (possibly due to a symmetry). When the dynamics within the invariant manifold are chaotic, the manifold often is only partially stable, in the sense that in an arbitrarily small neighborhood of the manifold, most trajectories are attracted to it but some trajectories are repelled. If noise is added to the system, the dynamics near the manifold may then be intermittent, with trajectories spending most of their time near the manifold but occasionally venturing far away. A scenario of particular interest is when the invariant manifold consists of states in which two or more coupled systems are behaving synchronously. The paper with Baek in Weather Forecasting and the papers with Restrepo under Dynamics on Networks also discuss synchronization of coupled systems.

Bifurcations and Periodic Windows

These papers study the parameter dependence of dynamical systems, considering both bifurcations at specific parameter values and the interplay between stable periodicity and chaotic behavior in parameter space as a whole. Several of the papers in Dynamics near Invariant Manifolds also are concerned with bifurcations.

Other Dynamical Systems Papers

Computational Genomics

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Updated: August 2005