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Thursday 18 May 2017Dynamics Seminar: Approximating stable manifolds of a saddle slow manifold in a bursting model

Hinke Osinga - Auckland

LSI Seminar Room A 14:30-16:00

Many models of neuronal activity exhibit complex oscillations in response to an input from a stimulus or other neurons in a network. The models are often in the form of a system of ordinary differential equations that exhibit different time scales. Analysis of such slow-fast systems uses geometric singular perturbation theory, which guarantees the existence of so-called slow manifolds. We consider the case of saddle slow manifolds and compute their associated stable (or unstable) manifolds. Based on manifold theory, geometric singular perturbation theory, and the theory of nonautonomous systems, we give a precise definition for a stable manifold of a saddle slow manifold and design an algorithm to compute it; our computational method is formulated as a two-point boundary value problem and uses pseudo-arclength continuation.

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