The primary goal of the research of Amitabha Bose is to derive and analyze mathematical models of neuronal activity. Primary applications include studies of the crustacean stomatogastric ganglion (STG). In particular, Bose and collaborators have developed models which explain how neurons in the pyloric network of the STG maintain phase relationships with one another as the frequency of network oscillations change (Manor, Bose, Booth and Nadim, 2003; Bose, Manor, Nadim, 2004). Other models explain how the frequency of the gastric mill rhythm is controlled by modulatory inputs to the STG (Ambrosio, Nadim, Bose; 2005). Bose is also interested in understanding the various roles that short-term synaptic plasticity can play in neruonal networks. He has shown how plasticity can give rise to bi-stability in oscillator-follower networks (Bose, Manor, Nadim; 2001) and how it can be used to explain the phenomena of episodic bursting in the context of frog ventilatory rhythmogenesis (Bose, Lewis, Wilson; 2005).

A second and developing interest is to understand how localized patterns of activity can arise in excitatory networks. In the figures below, two different activity patterns from a 1-dimensional array of neural oscillators coupled only be excitatory synapses are shown. In one, a wave of excitation spreads through the entire network causing all cells to eventually oscillate (time on vertical axis, neurons 1-20 on horizontal axis). Alternatively, in the other for a slightly smaller value of coupling strength, the excitation does not spread to the entire network and a stable bump solution is obtained in which only 7 neurons oscillate. Both simulations have the same initial conditions. Neurons 9, 10 and 11 were initially given a 50 msec jolt of excitation to initiate activity. Stable bumps are thought to be important in modeling working memory in which a bump would correspond to a recalled memory.

The existence of stable bumps in excitatory networks has recently been reported, but the mechanism by which the spread of excitation is stopped remained a mystery. Jonathan Rubin and I show that the spread of excitation can be curtailed due to slow passage near a saddle-node bifurcation (Rubin, Bose; 2004). The results show that the timing of synaptic inputs, and not just the strength of inputs, to a particular neuron determine whether or not it will fire. Thus while two adjacent neurons may receive excitatory inputs of equal strength, only one of the two may fire thereby stopping the spread of the excitatory wave.