Physics of Modes with Self-Organized Criticality at the Edge of Stability

Characteristics of modes and their physical properties in the region close to the point of bifurcations in systems with self-organized criticality are considered. A mathematical model of the synchronization of relaxation self-oscillations based on the modified Wiener–Rosenblueth axiomatic model and the properties of uniform almost-periodic functions is used to study the modes near the point of bifurcation. It is shown that a set of remarkable properties in the operating mode near the point of bifurcation can be achieved due to positive feedback while stabilizing it with negative nonlinear feedback.