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Bursting oscillations from a homoclinic tangency in a time delay system

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Destexhe, Alain | Gaspard, Pierre

Edité par CCSD ; Elsevier -

International audience. We describe a type of bursting oscillations arising in a model of reciprocally connected neurons, where a time delay has been introduced to account for synaptic and propagation delays. We show that in this system bursting oscillations appear at an infinite period bifurcation characterized by a homoclinic tangency to a limit cycle. Such homoclinic bursting phenomena are characterized by a logarithmic lengthening of the period, which could be measured from experimental time series.

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