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A Macroscopic Model of Neural Ensembles: Learning-Induced Oscillations in a Cell Assembly

A mathematical model is developed to characterize the aggregate behavior of large neural networks in which each individual neuron can be described by the general Hodgkin-Huxley format. Equations relating the average input activation and connection strength of the neurons to other ensemble parameters are derived using only the first and second order statistics of the system. The model describes the global effects of weight changes brought about by a local Hebb-type adaptation rule. In particular, such adaptation can lead to rhythmic behavior of ensemble activity even in an isolated cell assembly of homogeneous cells. Conditions that make such oscillatory behavior possible are identified and the frequency of oscillation is quantitatively related to the network parameters. Results from computer simulation support the mathematical analysis.