Place:Room An301, An Block,IIS, The University of Tokyo 
Speaker:Dr. Hongjun Cao (Department of Mathematics, Scheel of Science, Beijing Jiaotong University)
title:Bursting and synchronization of bursts in map-based neuron networks.

In this talk, first of all, a system consisting of two Rulkov map-based
neurons coupled through reciprocal electrical synapses is discussed. When
the electrical coupling is excitatory, the square-wave bursting can be well
predicted by the fast-low decomposing technique and the bifurcation analysis
of a comparatively
simple low-dimensional subsystem embedded in the invariant manifold. While,
when the synapses are inhibitory due to the artificial electrical coupling,
a fast-slow analysis is carried out by treating the two slow variables as
two different bifurcation parameters. The subsequent numerical simulations
demonstrate that there exists a kind of special elliptic bursting. The
occurrence of this kind of elliptic bursting is due to the interaction
between two chaotic oscillations with different amplitudes. Moreover, the
generation of antiphase synchronization of networks lies in the different
switching orders between two pairs of different chaotic oscillations
corresponding to the first neuron and the second neuron, respectively.
 Second, a general system consisting of two map-based Rulkov neurons coupled
through reciprocal excitatory or inhibitory chemical synapses is considered.
From the phase plane analysis point of view, we present the detailed
explanation concerning how excitatory synapses induce antiphase
synchronization, and that small variations in the synaptic threshold may
result in drastic variations in the synchronization of spikes within bursts.
Finally we show how the  synchronization effects found in the two-neuron
system extend to larger networks.

Keywords: map-based neuron model, neuron networks, bursting, synchronization