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Lecture 8: (U. of Cambridge): Oscillatory escape: a Non-Poissonnian escape process

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SDB - Stochastic dynamical systems in biology: numerical methods and applications

This lecture introduces novel concepts in asymptotic of second order PDE . It is a continuation of lecture 7. The motivation is coming from noisy dynamical systems, modelling neuronal networks with synaptic properties. The lecture presents a novel matched asymptotic, based on Mobius conformal mapping, Hopf normal form, to estimate the distribution of exit times and exit points (concentrated at one boundary point). The spectrum of the Fokker-Planck non-selfadjoint operator is computed. The role of the second eigenvalue is explained and generated the oscillation escape.



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