Piecewise Scaling in a Model of Neural Network Dynamics

Abstract

Realistic neural network (RNN) model was proposed in 1981 by Kropotov and Pakhomov [4] for description of most important neuro-physiological dynamical mechanisms. In the modified RNN (MRNN) model [1,3] the defined by the Bogdanov-Hebb principle dynamics of interneuron interactions and a dissipation were introduced. In results the dynamics of the system appeared to be more stable and also a possibility arose to investigate the structure processes. The stable regimes of the MRNN model can be classified as periodical and non-periodical ones. A special case of non-periodical regime is the critical dynamics. It is characterized by consequences of quasi-periodical patterns of neuron activity with mean value of one equal 1/2. The distribution of durations of the patterns of such a kind is presented by a piecewise potential function.