The Narrow Corridor of Stable Solutions in an Extended Osipov--Lanchester Model with Constant Total Population

Sergey Salishev

Papers from arXiv.org

Abstract: This paper considers a modification of the classical Osipov--Lanchester model in which the total population of the two forces $N=R+B$ is preserved over time. It is shown that the dynamics of the ratio $y=R/B$ reduce to the Riccati equation $\dot y=\alpha y^2-\beta$, which admits a complete analytical study. The main result is that asymptotically stable invariant sets in the positive quadrant $R,B\ge 0$ exist exactly in three sign cases of $(\alpha,\beta)$: (i) $\alpha 0$ or $\beta>0$ the solutions reach the boundaries of applicability of the model in finite time. Moreover, $\alpha

Date: 2025-12
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