Seminar Details
2014-04-01 (14.00) : Spectral operator-theoretic approach to dissipative systems: toward a systematic linear analysis of nonlinear systems ?
At Euler building
Organized by Mathematical Engineering
Speaker :
Mauroy, Alexandre
Abstract :
Operator-theoretic methods provide a powerful alternative description of dynamical systems. In particular, the so-called Koopman operator turns a nonlinear system into a linear (but infinite-dimensional) system that is amenable to spectral analysis. While the spectral properties of the Koopman operator have been extensively studied over the past decades in the case of conservative systems (i.e., on an attractor), we show in this talk that they are also useful for studying the global properties of dissipative systems (i.e., off the attractor). This will be illustrated through the concept of isochrons (which is of great importance in computational neuroscience). In this context, the operator-theoretic framework provides not only a new method for computing the isochrons but also an elegant way to extend them to other types of attractors. Finally, we will briefly explain how the framework might also yield a new approach to global stability analysis which mirrors the spectral stability analysis of linear systems.