Bifurcation criterion of faults in complex nonlinear systems

•One adopts a novel approach to identify faults in electric circuit systems.•One uses bifurcation results of corresponding amplitude and frequency (period) to analyze the universal characteristics.•The results will provide a bifurcation criterion of faults in complex nonlinear systems.•The research is not direct application of Feigenbaum theory, it will be helpful for the solution of the Blackout Problem.

In this paper, we introduce bifurcation theory into complex nonlinear systems. We adopt a novel approach to identify faults in electric circuit systems. After accidents occur without warning, with large numbers of complicated and high-precision calculations, we use bifurcation results of corresponding amplitude and frequency (period) to analyze their universal characteristics. Based on super attractive parameters, we have got the universal constant 4.6692… . The results from the present investigation imply that each fault in an electric circuit system must correspond to one or more bifurcation locations, which will provide a bifurcation criterion of faults in complex nonlinear systems. This research will have a significant theoretical value and engineering practical significance.