MODELING IRRITATIONS SPREADING IN RANDOM NETWORKS

Abstract

In today’s world there are many systems which are quite complex, both in structure and in the dynamics of the changes occurring in them. These systems have a general name - complex systems. In recent decades the complex systems have been presented by the so-called random networks where the system components work as nodes (vertices) and their interactions serve as connections (edges). Subsequently, in order to understand the complex systems, their topological peculiarities and behavior, random networks behind them should be studied.

At modeling some systems, for example, neuron networks, the study of certain properties of nodes such as the spread of the activity (irritation) in the network is of interest. To conduct such a study, to each node of the network is attributed a certain state, active or passive, and it is assumed that this state can change with time, simply by rest or by the transfer of the activity to the multitude of neighbors. The study of the process of the spread of irritations within the network is carried out through the trajectory of the irritation spread – the function of the concentration modification of active nodes in time.

The process of the spread of irritations in the classical Erdős-Rényi model random networks, as well as the issues of the computer simulation modeling of the latter are studied. Different modeling algorithms and certain tests of compliance with
the laws of classical kinetics are proposed for them on the basis of which, a comparative analysis is conducted with theoretical expectations in order to reveal the optimal algorithm.