Six-sector Lorenz model for critical infrastructure risk management

The work is dedicated to the problem of developing mathematical methods for assessing the vulnerability of critical infrastructure (CI). The main goal of the study is to create a mathematical model for forecasting crisis phenomena, ranking threat levels, and identifying weak links in CI that significantly affect the deformation of the security space. The model includes an economic block and a risk assessment block. The economic block is described by a six-sector Lorenz model with variable coefficients, which integrates similarly described economic sectors into a unified structure. Each sector is considered in terms of productivity, employment, and structural disruptions in sectors directly related to CI activities: energy, transport infrastructure, water supply networks and hydraulic structures, chemical industry, production, storage, and transportation of hazardous materials, as well as food and medical supplies, and information technology. The risk assessment block uses catastrophe theory methods to evaluate vulnerability of CI. Risk is assessed based on the proximity of the model parameters to their bifurcation values, upon reaching which the system transitions from a stationary state, characterized by acceptable vulnerability, to a state of increased vulnerability. The main results of the work are related to the numerical study of the developed model. The conditions for the transition of interconnected economic sectors to a regime of deterministic chaos, due to changes in specific demand and supply for production system outputs and the number of jobs in them, as well as changes in the rate of elimination of structural disruptions, have been identified. It has been shown that there are parameter value ranges in the model where minor changes lead to significant transformations in the CI system and its security. Further development of this work will focus on determining the dependence of the control parameters of the developed model on technological, environmental, economic, and social factors that characterize the functioning of CI.