Challenging “Structure Determines Function”: Configuration-Independent Synchronization Stability Boundary and Spontaneous Synchronization

Does structure and parameter determine function in complex coupled oscillator systems? Conventional theory of synchronization stability is built upon this premise, relying crucially on knowledge of network topology and system parameters. We challenge this view by discovering a universal synchronization stability boundary defined solely by the states of oscillators, which is independent of configuration (encompasses both the interaction topology and oscillator parameters). Through exhaustive validation in two disparate test systems and rigorous mathematical proof, we demonstrate that this boundary is rooted in physical reality, not in any specific model. Furthermore, a novel type of spontaneous synchronization, a non-equilibrium critical phenomenon, has also been discovered near this boundary and likewise exhibits configuration-independence. These findings challenge the structural basis of the synchronization stability boundary (a key function) on complex networks. They demonstrate that the loss of synchronization stability is governed by an intrinsic, configuration-independent critical condition. Consequently, our work challenges the theoretical foundation of the “from configuration to function” principle for predicting collective behaviors in complex systems.