Mathematics of battles and sanctions. Osipov-Lanchester battle models history

The talk is devoted to mathematical models of the dynamics of two opposing agents (countries, coalitions) under the conditions of recurring conflict situations (battles, introduction of sanctions and counter-sanctions, etc.). The history of the Osipov-Lanchester battle models is discussed. Based on the Osipov-Lanchester model, models of sanctions and counter-sanctions and conditions for their stability are proposed both for the case of complete information and under stochastic or nonlinear uncertainty. A controlled version of the sanctions and counter-sanctions model described by bilinear difference equations is proposed and the possibility of maintaining the stability of the models using small control actions isdiscussed. The results are interpreted in terms of maintaining international stability. The risks of global instability caused by the continuation of confrontation and the growth of the intensity of sanctions are formulated. Possible ways of stabilizing the international situation by means of small impacts based on mutual trust of the parties are discussed.
Most of the results are published in the paper: A. Fradkov. International Stability under Iterated Sanctions and Counter-sanctions.
IFAC-PapersOnLine, Vol 56, Is 2, 2023, pp 11010-11014. https://doi.org/10.1016/j.ifacol.2023.10.800
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