Pulse-coupled Oscilators

In addition to the well known fully synchronized state and the splay state, there exist clustered states, limit cycles and the so-called (N-1,1) state where nearly all oscillators are synchronized except for one outlier. With the aid of index theory and high-precision numerical simulations, the complete bifurcation sequences of these attractors and other fixed points are found for N ≤ 4.

2. A Spike-timing-based Algorithm for Mamalian Olfaction

We investigate extensions to the model put forward by Brody and Hopfield for spike-timing based pattern recognition applied to mammalian olfaction. This model implements a pattern recognition algorithm realized in the dynamics of a network of coupled IF neurons subject to a sine-wave rhythm. Subsets of these neurons can synchronize through the principle of one-to-one mode locking.

Bolun Chen, J.R. Engelbrecht, R. Mirollo. BMC neuroscience 15 (S1), P90

The network represents 3 layers of neural activity, the first two of which are inspired by the connectivity of glomeruli and mitral cells in mammalian olfactory circuits and the gamma-rhythm activity observed in the olfactory bulb. Specifically in this model a pattern of glomerular activity representing a given odor causes a particular subset of model mitral cells to synchronize and this synchronous activity can drive a "grandmother" model cortical cell through threshold triggering a recognition event.

In this study we quantify the performance of their original model and compare it to our extensions of the model such as using a network-generated rhythm rather than a sine-wave, introducing inhibitive feedback and generalizing to p-q mode locking strategies. We compute the scaling with respect to the number of mitral neurons of a measure of the number of odor patterns the model can recognize. Quite remarkably we find this performance can increase very fast with increasing network size consistent with exponential scaling.