Transient spike adding in the presence of equilibria
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
Received: 21 December 2015
Revised: 20 March 2016
Published online: 22 November 2016
Many models of neuronal activity exhibit complex oscillations in response to an input from other neurons in a network or to an input from a stimulus. We consider the effect of a single short stimulus on a simple model designed to mimic some features of neuronal dynamics. We focus on the transient response induced by the stimulus, particularly on the spike-adding behaviour of the response. Our main goal is to explain how the transient response is affected by the presence of unstable equilibria. We also investigate the dependence of the number of spikes on the amplitude and duration of the stimulus. In our analysis, we use numerical continuation methods and exploit the presence of different time scales in the model.
© EDP Sciences, Springer-Verlag, 2016