Spontaneous state switching in realistic mean-field model of visual cortex with heteroclinic channel
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KeywordsVisual Cortex Pyramidal Neuron Sigmoid Function Visual Input Inhibitory Interneuron
Spontaneous switching between cortical states in the visual cortex of cat was reported by Kenet et al.: a succession of spatial activation patterns normally associated with visual input was observed even in the absence of external input. Using a Wilson-Cowan network, Blumenfeld et al. proposed a model for this phenomenon that generated multistability by applying unstructured noise. Here we use the biologically realistic mean-field model of Jansen & Rit , together with the heteroclinic channel theory proposed by Rabinovich et al., cf. Ref. , to propose a mechanism how such spontaneous switching between states could occur independent of extrinsic noise.
[Θ: 2nd order differential operator, V: membrane potentials, W: connectivity, S: sigmoid function, I: input, K: gain]
Evoked activity was simulated by applying input to a specific hypercolumn, yielding patterns that are very similar to the OPC distribution maps - compare Fig. 1C(Evok.) with 1C(IV,V). Importantly however, even without any external stimulus the system spontaneously switches from one state to another, see Fig. 1C(Spon.). In state space the system evolves in a heteroclinic channel, made up by the trajectories near a chain of saddle points (representing the OPCs) and associated unstable separatrixes. The inhibitory connectivity governs this sequence of activation. Imposing noise on this connectivity can introduce randomness into the sequence of activation.
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