Mathematical modeling reveals complex bifurcations and periodic cycles in counterinsurgency dynamics, indicating that collateral damage fundamentally alters victory and defeat boundaries.
In this article, by extending the existing scholarship on the Lanchester model in asymmetric conflicts, particularly counterinsurgency, we introduce a novel class of collateral damage curves with specific mathematical features, including saturation and non-monotonicity. The interaction between the harmed population and active insurgents will create conditions for the emergence of a Hopf bifurcation that depends on insurgents' firepower, government recruitment, and intelligence rate. Furthermore, given the characteristics of the collateral damage functions, the possibility of multiple equilibria in our conflict model, along with periodic solutions, can lead to a homoclinic bifurcation and to non-trivial boundaries for victory/defeat in the conflict.
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Aghaieebeiklavasani et al. (2026) studied this question.
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