UCLA

Self-organized criticality is a ubiquitous phenomenon that appears in many complex dynamical systems. During this special phase, the system experiences long-range correlation in space and in time. In order to understand its origin, we developed a method that can predict whether or not a stochastic dynamical system will be chaotic. We hypothesize that self-organized criticality and chaos originate from breaking the supersymmetries of the complex dynamical systems; therefore, the eigenvalue spectrum for the Fokker-Planck Hamiltonian should have pairs of complex eigenvalues on its imaginary axis. By applying the Fokker-Planck equation to the Chua oscillator, we show that the eigenvalues move closer to the imaginary axis as the system becomes chaotic. Also, we built a self-organized critical circuit using CMOS transistors. The circuit exhibits "avalanche" behaviors, in which groups of oscillators become out of synchronization together. The avalanche statistics show power laws in both avalanche size and inter-avalanche time.