Mezić Research Group

Dynamical Systems and Nonlinear Control Theory

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The Effect of Symmetry on Spatiotemporal Resonances in Coupled Systems

Bryan Eisenhower

Conformation change

In this work we study instability in networked systems which leads to a better understanding of their sensitivities and control requirements. The networks we study range from those inspired by biology to power grids and networked control systems. We use both deterministic and stochastic Dynamical Systems tools including high dimensional internal resonance, Hamiltonian dynamics, averaging, and analysis of stochastic differential equations.


Security, efficiency, and performance is driving engineering designs to be more networked than they have been in the past. These vast networks may contain multiple conformations and specific instabilities in the network are needed to switch between these conformations. Because these instabilities exist in the dynamics, tools are needed for their analysis to ensure that the systems is robust to common environmental disturbance. In our work we study a networks of oscillators which possess at least two global equilibria. These networks range from biologically motivated to power grids, or coordinated control networks. We analyze the re-conformation process as both a noise activated instability and one which is initiated by structural perturbation. Drawing from dynamical systems tools and chemical reaction theory we predict both energy requirements and rates of the activation process in both stochastic and noise free environments.

Last Updated on Saturday, 25 April 2009 10:02  

Acknowledgements