Transient bifurcations in neural error correction

This paper presents an investigation into the responses of neurons to errors in presynaptic spike trains. Errors are viewed, in nonlinear dynamical terms, as brief-duration changes in stationary presynaptic spike trains which induce transient responses in the postsynaptic cell. As these are generally large-magnitude transients, linearized neural models are not helpful. Instead, the responses of a full, nonlinear physiological model of a neuron that includes the recognized living prototype of an inhibitory synapse are analyzed. More specifically, the transients are examined in the context of the stationary behaviors that precede and succeed each error. It is shown that one and two dimensional bifurcation diagrams can be constructed from the transient responses—that there are marked changes in the transient responses at points that correspond to bifurcations in the stationary responses, qualitative changes in transients on either side of bifurcations, and only quantitative changes in transients between bifurcations.