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* To whom correspondence should be addressed. E-mail: edmund.rolls{at}psy.ox.ac.uk.
Recent neurophysiological experiments have led to a promising "biased competition hypothesis" of the neural basis of attention. According to this hypothesis, attention appears as a sometimes non-linear property that results from a top-down biassing effect that influences the competitive and cooperative interactions that work both within cortical areas and between cortical areas. In this paper we describe a detailed dynamical analysis of the synaptic and neuronal spiking mechanisms underlying biased competition. We perform a detailed analysis of the dynamical capabilities of the system by exploring the stationary attractors in the parameter space via a mean field reduction consistent with the underlying synaptic and spiking dynamics. The nonstationary dynamical behaviour, as measured in neuronal recording experiments, is studied via an integrate-and-fire model with realistic dynamics. This elucidates the role of cooperation and competition in the dynamics of biased competition; and shows why feedback connections between cortical areas need optimally to be weaker by a factor of approximately 2.5 than the feedforward connections in an attentional network. We modelled the interaction between top-down attention and bottom up stimulus contrast effects found neurophysiologically, and showed that top-down attentional effects can be explained by external attention inputs biassing neurons to move to different parts of their non-linear activation functions. Further, it is shown that although NMDA non-linear effects may be useful in attention, they are not necessary, with non-linear effects (which may appear multiplicative) being produced in the way just described.
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