A one-dimensional chain of mutually inhibitory spiking neural oscillators with spike propagation delay is presented which can robustly distinguish gradients in one-dimensional inputs, for instance in an image segmentation scenario. The mechanism uses an oscillator death caused by a gradient in the input to create regions of near-uniform phase in the spike-train outputs of the network, with a clear phase difference between regions. The boundaries between these crisply defined regions correspond to the steepest gradients in the image inputs, with a sensitivity determined principally by the spike propagation delay. Thus the network can be seen as smoothing heterogeneity in input data. The mechanism relies on a biologically plausible coding of the inputs by the inter-spike intervals of a set of spike bursts, and on coding the outputs by the phase difference between the two regions created.
This work extends studies of synchronisation and oscillator death for networks of integrate-and-fire neurons with delayed mutually inhibitory connections in two ways. Firstly, it is shown that any robustness in the mechanism is possible only when shunting in the synaptic inputs and absolute refractoriness are included in the model. Secondly, analysis of both the transient and long term steady state behaviour of the network remains possible even with these added features and realistic coding. The analysis accurately predicts parameter regimes within which the network works robustly for a wide range of inputs, whilst guaranteeing the stability of the state of oscillator death for large times.
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