Threshold models of warfare

Modified models of the conduct of hostilities by Lanchester - Osipov are studied, in which three variants of the psychological characteristics of agents are taken into account: surrender, evasion of the struggle against its possible resumption, and conformal desertion. For the first two options, the threshold model of Schelling's limited partnership is used; for the latter, the threshold model of Granovetter's conformal behavior. So, the agent has a threshold in relation to the proportion of “ours” deserting from the battlefield. If this fraction is greater than the threshold, then the agent also joins the runaways (here the threshold corresponds to the level of his discipline). For modification, the distribution functions of the thresholds of conformity of agents were used. The two-parameter beta function with the distribution density x1-a(1-x)1-b. is selected as the distribution function. This is due to the fact that its parameters allow meaningful interpretation of such characteristics as the ratio of "cowards" and "brave men" of the fighting parties. So, the more a, the more “cowardly” agents in the group. The more b, the more “bold” agents in the group. In each of the models, the ODE system was numerically solved for a certain threshold distribution function, the dynamics of the number of agents participating in the battle were plotted, and the results were analyzed.