Model of the Information Shock Waves in Social Network Based on the Special Continuum Neural Network

The article proposes a special class of continuum neural network with varying activation thresholds and a specific neuronal interaction mechanism as a model of message distribution in social networks. Activation function for every neuron is finded as a decision of the specific systems of differential equations which describe the information distribution in the chain of the network graph. This class of models allows to take into account the specific mechanisms for transmitting messages, where individuals who, receiving a message, initially form their attitude towards it, and then decide on the further transmission of this message, provided that the corresponding potential of the interaction of two individuals exceeds a certain threshold level. The authors developed the original algorithm for calculating the time moments of message distribution in the corresponding chain, which comes to the solution of a series of Cauchy problems for systems of ordinary nonlinear differential equations.