Interpreting A Period-Adding Bifurcation Scenario In Neural Bursting Patterns Using A Discontinuous Map

In neurodynamics, the firing rhythmic patterns (i.e. the temporal patterns of the inter-spike intervals (ISIs) of action potentials) of neurons is thought to play fundamental roles in information processing of neurons, so it is very important to study the generation of ISI and the dynamical mechanism of changes of ISI with respect to parameter.The experiments of neuronal pacemaker show typical bifurcations from period 1 to period 5 with stochastic bursting patterns. A discontinuous map of the slow variable in Chay model which captures the essential characters of the period-adding bifurcation scenario is constructed in this thesis. These stochastic bursting patterns are reproduced and explained by adding the term of noise to Chay model and the constructed map. Furthermore, based on the discontinuity of the map, the dynamical mechanism of the period-adding bifurcation scenario is illustrated by border-collision bifurcation.