We model insurgency and counter-insurgency (COIN) operations with a large-scale system of differential equations and a dynamically changing coalition network. We use these structures to analyze the components of leadership, promotion, recruitment, financial resources, operational techniques, network communications, coalition cooperation, logistics, security, intelligence, infrastructure development, humanitarian aid, and psychological warfare, with the goal of informing today's decision makers of the options available in COIN tactics, operations, and strategy. In modern conflicts, techniques of asymmetric warfare wreak havoc on the inflexible, regardless of technological or numerical advantage. In order to be more effective, the US military must improve its COIN capabilities and flexibility to match the adaptability and rapid time-scales of insurgent networks and terror cells. Our simulation model combines elements of traditional differential equation force-on-force modeling with modern social science modeling of networks, PSYOPs, and coalition cooperation to build a framework that can inform various levels of military decision makers in order to understand and improve COIN strategy. We show a test scenario of eight stages of COIN operation to demonstrate how the model behaves and how it could be used to decide on effective COIN resources and strategies.

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Mobile ad hoc sensor networks often need cooperation-sensors working together to achieve their common goal. How does cooperation help mobile autonomous sensors position themselves in effective locations? This paper uses mathematical simulation to study this question about sensor deployment and efficiency. The goal is to distribute sensors over a region of interest in the plane in a balanced way to ensure uniform coverage and equalized load. This paper generalizes an algorithm for accomplishing this in a distributed, cooperative, computationally efficient manner, while also allowing for a generalized notion of balance for nonhomogeneous zones and variable-capable sensors (i.e., some zones are more important than others and some sensors are more capable than others).