Methods for determining the equilibrium state of a network with given flows in nodes of information networks of cyber-physical systems

Abstract

Background. The multidimensionality of cyberspace and the high level of informatization of critical infrastructure objects, both in Ukraine and globally, pose a threat to humanity at the global level in the foreseeable future. The situation is complicated by the fact that critical infrastructure objects, which operate within a unified information space and support a wide range of modern information technologies, remain vulnerable to new types of threats, despite tremendous efforts to counteract external cyber intrusions.
Methods. It has been identified that the study of complex systems employs modern mathematical methods such as topology, graph theory, and linear algebra.
Results. The entropic method for analyzing complex systems has found wide application in practical problems related to the study of natural, technical, and cyber-physical systems. This method has long been used to develop efficient systems for coding, encryption, and information protection. With the increase in computational power, the practical value of researching dynamic systems – including those based on entropy – has grown, as entropy serves as a good indicator for selecting certain states of a system from the set of all its possible states.
Conclusions. Since the study of structures and general patterns is common across many branches of science and technology, tasks of a general nature – where the specific nature of the system is not taken into account – remain relevant. This study presents an algorithm for determining the state of a multi-node information flow network in which its entropy reaches a maximum value. The algorithm is based on analytical expressions for entropy and its first and second derivatives, derived by the authors and defined on the set of kernel solutions of a system of linear equations to which the original problem is reduced. Experimental results are presented for determining the solution set and solving the optimization problem of finding the state with the maximum entropy value for networks with 3, 4, 5, and 6 nodes. Possibilities for further improvement of the method for calculating more complex networks are analyzed.