Bursting oscillations from a homoclinic tangency in a time delay system.
Alain Destexhe and Pierre Gaspard

Physics Letters A 173: 386-391, 1993.

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The authors describe a type of bursting oscillation arising in a model of reciprocally connected neurons, where a time delay has been introduced to account for synaptic and propagation delays. They 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.