Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators

It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered. (c) 2008 American Institute of Physics.

Single-neuron recordings from behaving primates have established a link between working memory processes and information-specific neuronal persistent activity in the prefrontal cortex. Using a network model endowed with a columnar architecture and based on the physiological properties of cortical neurons and synapses, we have examined the synaptic mechanisms of selective persistent activity underlying spatial working memory in the prefrontal cortex. Our model reproduces the phenomenology of the oculomotor delayed-response experiment of Funahashi et al. (S. Funahashi, C.J. Bruce and P.S. Goldman-Rakic, Mnemonic coding of visual space in the monkey's dorsolateral prefrontal cortex. J Neurophysiol 61:331-349, 1989). To observe stable spontaneous and persistent activity, we find that recurrent synaptic excitation should be primarily mediated by NMDA receptors, and that overall recurrent synaptic interactions should be dominated by inhibition. Isodirectional tuning of adjacent pyramidal cells and interneurons can be accounted for by a structured pyramid-to-interneuron connectivity. Robust memory storage against random drift of the tuned persistent activity and against distractors (intervening stimuli during the delay period) may be enhanced by neuromodulation of recurrent synapses. Experimentally testable predictions concerning the neural basis of working memory are discussed.