Strategic Reserve Systems: Nonlinear Capacity Modeling and Stability of Critical Supply Networks

Abstract Strategic reserve systems, including food, medical supplies, and critical equipment, are essential for maintaining societal stability under crisis conditions. Traditional planning approaches rely on linear demand assumptions and static capacity constraints, which fail to capture nonlinear dynamics arising during systemic stress. This work develops a nonlinear mathematical framework for modeling reserve systems as capacity-constrained dynamical processes. A coupled system of differential equations is introduced to describe the interaction between demand amplification and dynamic capacity depletion. A dimensionless instability functional is defined to characterize system resilience. It is shown that instability occurs when nonlinear demand exceeds available capacity within finite time. The framework provides a basis for designing resilient reserve systems under uncertainty and shock conditions.