UBC Theses and Dissertations
Stochastic phase dynamics of noise driven synchronization of uncoupled conditional coherent oscillators Thompson, William F.
We consider a pair of uncoupled conditional oscillators near a subcritical Hopf bifurcation that are driven by two weak white noise sources, one intrinsic and one common. The effect of the competition between the common and intrinsic noise forcing on the synchronization behaviour of the phases of these two oscillators is studied. Using a stochastic multiple scales method, we derive the envelope equations of the oscillators and then use the theory of linearized stochastic differential equations as well as an asymptotic analysis to study the probability density of the phase difference of the oscillators. It is found that common noise increases the degree of synchrony in the pair of oscillators and that it can be characterized by the ratio of intrinsic to common noise. Furthermore, the nonlinear dynamics of the oscillators can affect the character of this synchronization in terms of the average phase difference. The results are also related to the study of spike time reliability and possible implications are brieﬂy discussed.
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