## UC Berkeley / Lawrence Berkeley Laboratory

#### Dimension reduction: From Soliton Dynamics to Neural Networks

**Eli Shlizerman, University of Washington**

##### April 20th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

The interplay between coherence and decoherence through subtle dynamics is a
widespread phenomenon across applications and is often modeled by nonlinear
PDEs or as large systems of ODEs. Derivation of low dimensional models that
retain these dynamics can give rise to the identification of the responsible
mechanisms for these phenomena. In this talk I will present the dimension
reduction methods that we have developed for near-integrable, dissipative
nonlinear PDEs and neural network models. The analysis of the outcome models
allows us to characterize synchrony, localized structures and instabilities in
these systems. In particular, I will describe the route to spatio-temporal
chaos in the forced nonlinear Schrodinger equation, the onset of multi-pulsing
in mode-locked lasers, and the mean-voltage for coupled conductance-based
neurons. The common ground for these problems is that the reduced models
faithfully capture the bifurcation structure. A detailed study of these models
leads to an explanation of the observed behavior and reveals novel regimes.