In this paper, we propose and analyze a new descriptive model of armed conflicts among N groups. The model is composed of \(N^2\) ordinary differential equations, with \(3(N^2+N)\) constant parameters that describe military characteristics and recruitment policies, ranging from pure defensivism to pure fanaticism. The results are only preliminary, but point out interesting (though not very surprising) properties: periodic coexistence is possible, and multiple attractors can exist; governmental groups cannot go extinct if they are highly defensivist, and rebels cannot be eradicated if they are highly fanatic. Shocks due to interventions of short duration of an external army can stabilize/destabilize the system and/or eradicate some group, and the same holds true for small structural changes. Other more subtle questions concerning, for example, the existence of chaotic regimes and the systematic evaluation of the role of strategic factors like power, intelligence, and fanaticism, remain open and require further research.
Mathematical modeling Social systems Conflicts Terrorism Bifurcations Chaos