Modeling Chemical Modulation Of Neural Processes

We analyse the effect of chemical neuro-modulation on collective processes in Ising spin neural networks with separable Hebbian-type synaptic interactions. Neuro-modulation is taken into account in the simplest way: a modulator-specific subset of neurons is prevented from transmitting signals. However, the presence of neuro-modulators is taken into account also during the learning stage, which leads to non-symmetric interaction matrices. We derive (in the limit of infinite system size) the macroscopic laws that determine the system's evolution in time at the level of order parameters. These laws are very transparant and show that, within the proposed framework, one can understand the functioning of neuro-modulators as follows: their role is to choose a particular mode of operation from a repertoire of learned behaviour. By considering specific examples of learning stages we indicate how neuro-modulation might be used by the brain as an extra degree of freedom for (a) performing selective pattern reconstruction, (b) controlling the reproduction speed of stored pattern sequences or (c) choosing a particular path from a set of partially overlapping stored trajectories through the state space (at points where the trajectories separate).