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Noise Driven Transitions between Stable Equilibria in Stochastic Dynamical Systems

dc.contributor.author Daniels, Kaitlin
dc.date.accessioned 2011-05-13T12:59:30Z
dc.date.available 2011-05-13T12:59:30Z
dc.date.issued 2011-05-13
dc.identifier.uri https://hdl.handle.net/10161/3751
dc.description.abstract In this paper we examine two specific models of dynamical systems in which noise plays a central role. The first is a stochastic differential equation (SDE) modeling a particle in a potential well; the second is a simplified version of the Morris-Lecar model of a neuron. In each case, we consider both the underlying deterministic dynamical system, which is a governed by an ordinary differential equation, as well as the randomly-perturbed dynamical system, whose solution is a stochastic process satisfying a stochastic integral equation. We investigate the how perturbations of the drift functions influence transitions between stable equilibria and what effects such perturbations may have on exit times. We compare the results from computer simulations to analytical derivations of expected exit times. These results contribute to the understanding of the forces driving transitions between stable equilibria in perturbed dynamical systems.
dc.language.iso en_US
dc.subject stochastic differential equations
dc.subject double well potential
dc.subject Morris Lecar model
dc.title Noise Driven Transitions between Stable Equilibria in Stochastic Dynamical Systems
dc.type Honors thesis
dc.department Mathematics


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