Exposure-Driven Gain Crossing and Post-Threshold Dynamics in Nonlinear Systems
How a System’s Own History Builds Internal Gain and Activates New Dynamical Behavior Nonlinear systems often change behavior only after coupling, control gain, or another internal influence becomes strong enough to cross a critical threshold. But how can this transition occur when the gain is not changed from outside? This paper develops a general framework […]
Accumulation-driven synchronization in phase oscillators
How Repeated Moments of Alignment Build Coupling and Lead Drifting Systems Into Synchronization This paper studies how synchronization can emerge even when a system begins in a state where synchronization is not immediately possible. In classical phase-oscillator models, drifting systems remain unlocked unless coupling is already strong enough to overcome detuning. Here, the coupling is […]
The Compatibility–Integration Cascade
How Internal Compatibility Strengthens Coupling and Stabilizes Complex Systems Complex systems often become stable only when the connections between their parts grow strong enough to overcome internal differences. But where does that added strength come from if the structure itself doesn’t change? This work introduces a general architecture where stability emerges from within: as subsystems […]