  Noise appears in the brain due to various sources, such as ionic channel
fluctuations and synaptic events. They affect the activities of the brain and
influence neuron action potentials. Stochastic differential equations have been
used to model firing patterns of neurons subject to noise. In this work, we
consider perturbing noise in the adaptive exponential integrate-and-fire (AEIF)
neuron. The AEIF is a two-dimensional model that describes different neuronal
firing patterns by varying its parameters. Noise is added in the equation
related to the membrane potential. We show that a noise current can induce
continuous and noncontinuous transitions in neuronal interspike intervals.
Moreover, we show that the noncontinuous transition occurs mainly for
parameters close to the border between tonic spiking and burst activities of
the neuron without noise.
