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On generic steady and dynamic tuning properties in neural field models with rectifying rate functions
Localized steady state activation profiles ("bumps") in neural field models have been proposed as computational models for orientation tuning functions of simple cells in area V1. In the present work, we show that such profiles generically reveal a constant tuning width and a linear amplitude response when the input intensity is varied. This holds for all neural field models that reveal localized activation profiles at all and that have only semilinear rate functions with thresholds equal to zero. Other details of the models are unimportant, for instance, the number or dimension of the model layers, or the precise form of the input profiles or connectivity kernels. Thus, steady state solutions of neural field models cannot unambiguously distinguish between feedforward and feedback mechanisms for orientation tuning only from amplitude responses and tuning widths at different contrast levels. We further show that also spatio-temporal solutions of neural field models have the property that they scale linearly with input strength but are otherwise forminvariant. This only requires the additional assumption that the postsynaptic membrane responses are linear. We argue that mechanisms underlying cortical tuning might come out clearer, when temporal responses are considered and not just steady states. Results in this paper are kept general and may also be applicable to tuned cortical activity in other contexts than orientation tuning.