The planar Lanchester model of insurgent warfare: Intricate Collateral Damage Functions and Global Bifurcation
One of the most notable aspects of mathematical modeling is that it sheds light on the complexities arising from changes in parameters and their real-world implications, thus gaining better insight into the dynamics of economic, political, and security phenomena. Moreover, modifications to mathematical modeling will set the stage for embedding new features into the system and enriching the assessment of our analysis. In the case of the Lanchester model of warfare, the introduction of the collateral damage function was an attempt to turn the model into a more realistic framework for understanding counter-insurgencies and irregular battles. In this article, we focus on addressing the impact of sophisticated collateral damage functions in a modified Lanchester model of combat, which reflects the multifaceted nature of warfare. This analysis shows the possibility of global bifurcations and their repercussions for the combat situation between two players. Finally, we assess the codimension two bifurcation analysis of our system based on the interaction between collateral damage and the effectiveness of targeting insurgents.