Analyzing the Stability of Lanchester Warfare Models for Symmetric Warfare Scenarios

This study analyzes the stability of Lancaster-type ODE models in symmetric warfare situations. In symmetric warfare situations, when the lethality coefficients (K) are equal for both forces in battle, the system exhibits marginal stability, characterized by poles at ± K, indicating that the model is stable in some regions and unstable in others. The present research illustrates a controlled rhythmicity, and these forces show a harmonized balance between the two battling forces in order to develop a strong strategy and decision for military.