Emergence of self-organized criticality and phase transition in the Olami-Feder-Christensen model with a single defect.

We examine the conditions for the emergence of self-organized criticality in the Olami-Feder-Christensen model by introducing a single defect under periodic boundary conditions. Our findings reveal that strong localized energy dissipation is crucial for self-organized criticality emergence, while weak localized or global energy dissipation leads to its disappearance in this model. Furthermore, slight dissipation perturbations to a system in a self-organized criticality reveal a novel state characterized by a limit cycle of distinct configurations. This newly discovered state offers significant insights into the fundamental mechanisms governing the emergence of self-organized criticality.