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Experimental evidence suggests that the computational state of corticalsystems change according to behavioral and stimulus context. However, it isstill unknown what mechanisms underlie this adaptive processing in corticalcircuitry. In this paper, we present a model of randomly coupled supercriticalAndronov-Hopf oscillators which can act as an adaptive processor by exhibitingdrastically different dynamics depending on the value of a single networkparameter. Despite being only composed of supercritical subunits, the fullsystem can exhibit either supercritical or subcritical Andronov-Hopfbifurcations. This model might provide a novel mechanism for switching betweenglobally asymptotically stable and nonhyperbolic neural network types inpattern recognition theory.

Emergence of Subcritical Bifurcations in a System of Randomly Coupled  Supercritical Andronov-Hopf Oscillators: A Potential Mechanism for Neural  Network Type Switching