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Tom Witelski : Perturbation analysis for impulsive differential equations: How asymptotics can resolve the ambiguities of distribution theory

Models for dynamical systems that include short-time or abrupt forcing can be written as impulsive differential equations. Applications include mechanical systems with impacts and models for electro-chemical spiking signals in neurons. We consider a model for spiking in neurons given by a nonlinear ordinary differential equation that includes a Dirac delta function. Ambiguities in how to interpret such equations can be resolved via perturbation methods and asymptotic analysis of delta sequences.

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