Root cause analysis on the deterministic unpredictability in chaotic systems

Several crucial problems, such as the forming mechanism of chaotic attractors and the root cause of the sensitive dependence on initial conditions, are researched in this work. The attractability of chaotic attractors is closely related to the existence of attractive plane in phase space of chaotic system. Each chaotic motion comprises at least two nonlinear motion modes. The essential reason for the sensitive dependence on initial conditions and form chaotic attractor is nonperiodic and asynchronous switch between two modes.