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# Weakly Connected Quasi-periodic Oscillators, FM Interactions, and Multiplexing in the Brain

@article{Izhikevich1999WeaklyCQ, title={Weakly Connected Quasi-periodic Oscillators, FM Interactions, and Multiplexing in the Brain}, author={Eugene M. Izhikevich}, journal={SIAM Journal of Applied Mathematics}, year={1999}, volume={59}, pages={2193-2223} }

- Published 1999 in SIAM Journal of Applied Mathematics
DOI:10.1137/S0036139997330623

We prove that weakly connected networks of quasi-periodic (multifrequency) oscillators can be transformed into a phase model by a continuous change of variables. The phase model has the same form as the one for periodic oscillators with the exception that each phase variable is a vector. When the oscillators have mutually nonresonant frequency (rotation) vectors, the phase model uncouples. This implies that such oscillators do not interact even though there might be physical connections between… CONTINUE READING

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