Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Nonlinear Dynamics I

DY 17.3: Talk

Wednesday, March 16, 2011, 11:00–11:15, ZEU 255

Nonlocal Generalized Models — •Christian Kuehn and Thilo Gross — MPI-PKS, Dresden

Generalized models have been applied successfully to understand the local dynamics of ordinary differential equations (ODEs) in equilibrium when the explicit functional forms of the ODE are only partially known. Hence the method is particularly successful in the context of biophysical problems. Generalized models allow us to draw conclusions about a large set of dynamical systems simultaneously using classical techniques from bifurcation analysis. In this talk, I will illustrate the mathematical and physical framework for generalized modeling and show that the method naturally applies to partial, stochastic and delay differential equations. Furthermore, a major extension to the analysis of periodic solutions will be introduced for ODEs. This new development marks the first step to a non-local dynamical analysis which is indispensable in many applications. The theory will be illustrated with a planar model system.