Physical Sciences and Mathematics Commons^™

Mechanisms Of Multistability In Neuronal Models, Tatiana Malashchenko

Physics and Astronomy Dissertations

Multistability is a fundamental attribute of the dynamics of neuronal systems under normal and pathological conditions. The mechanism of bistability of bursting and silence is not well understood and to our knowledge has not been experimentally recorded in single neurons. We considered four models. Two of them described the dynamics of a leech heart interneuron: the canonical model and a low-dimensional model. The other two models described mammalian pacemakers from the respiratory center.

We investigated the low-dimensional model and identified six different types of multistability of dynamical regimes. We described six generic mechanisms underlying the co-existence of oscillatory and silent …

A Mechanism Of Co-Existence Of Bursting And Silent Regimes Of Activities Of A Neuron, Tatiana Igorevna Malashchenko

Physics and Astronomy Theses

The co-existence of bursting activity and silence is a common property of various neuronal models. We describe a novel mechanism explaining the co-existence of and the transition between these two regimes. It is based on the specific homoclinic and Andronov-Hopf bifurcations of the hyper- and depolarized steady states that determine the co-existence domain in the parameter space of the leech heart interneuron models: canonical and simplified. We found that a sub-critical Andronov-Hopf bifurcation of the hyperpolarized steady state gives rise to small amplitude sub-threshold oscillations terminating through the secondary homoclinic bifurcation. Near the corresponding boundary the system can exhibit long …