Core-halo instability in dynamical systems

This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes unstable. The threshold occurs at the point at which flows and interactions between subsystems (surface' effects) overwhelm internal stabilizing dynamics (volume’ effects). The theorem is used to identify instability thresholds in systems that possess a core-halo or core-periphery structure, including the gravo-thermal catastrophe – i.e., star collapse and explosion – and the interbank payment network. In the core-halo model, the same dynamical instability underlies both gravitational and financial collapse.