Comment on "Long Time Evolution of Phase Oscillator Systems" [Chaos 19,023117 (2009), arXiv:0902.2773]

A previous paper (arXiv:0902.2773, henceforth referred to as I) considered a general class of problems involving the evolution of large systems of globally coupled phase oscillators. It was shown there that, in an appropriate sense, the solutions to these problems are time asymptotically attracted toward a reduced manifold of system states (denoted M). This result has considerable utility in the analysis of these systems, as has been amply demonstrated in recent papers. In this note, we show that the analysis of I can be modified in a simple way that establishes significant extensions of the range of validity of our previous result. In particular, we generalize I in the following ways: (1) attraction to M is now shown for a very general class of oscillator frequency distribution functions g(\omega), and (2) a previous restriction on the allowed class of initial conditions is now substantially relaxed

The Politics of Empire: The United States and the Global Structure of Imperialism in the Early Twenty-First Century

In the field of diplomatic history, scholars have debated how the United States has played an imperial role in the world. Although diplomatic historians have presented many different interpretations, they have never agreed on the defining aspects of U.S. imperialism. My dissertation intervenes in the debate by reviewing how the United States functioned as an imperial power at the start of the twenty-first century. In my dissertation, I make use of a wide array of publicly available sources, including the public remarks of U.S. officials, the public records of the U.S. government, and the diplomatic cables published by WikiLeaks, to describe how the United States enforced a global system of imperial order. Specifically, I argue that officials in the administrations of George W. Bush and Barack Obama began the twenty-first century by implementing an imperial grand strategy to keep the international system organized around a dominant center and a subordinate periphery in a global structure of imperialism. By showing that officials in both the Bush and Obama administrations kept each region of the world integrated into a global structure of imperialism, my dissertation intervenes in one of the key debates in diplomatic history to define how the United States functioned as an empire

Synchronization in large directed networks of coupled phase oscillators

We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed positive/negative coupling strengths. We compare our theory with numerical simulations and find good agreement