Tatiana Prudnikova: Noisy dynamics of a neuron with co-existing spiking and resting states

BCCN Berlin / TU Berlin

It is known that transition between resting and spiking states of a single neuron is in some cases associated with emergence of a limit cycle and simultaneous disappearance of resting state equilibria (e.g. a saddle-node on invariant circle bifurcation). We study a two-dimensional conductance based neuron model, which under certain parameter ranges has co-existing stable limit cycle and stable node, i.e. resting and spiking states exist at the same time. This can be reached through saddle homoclinic orbit bifurcation (also known as simply homoclinic bifurcation) by changing different parameters. In this work we use the time constant of potassium ion channel conductance. As we assume a noisy input to the neuron, the system can switch between resting and spiking states and thus execute different spiking patterns. We study transition between the patterns, show what different spiking timescales might be, and try to understand the shape of the interspike interval histogram.

Additional Information

Master thesis defense in the International master program Computational Neuroscience

Organized by

Susanne Schreiber / Robert Martin