New scheme of anticipating synchronization for arbitrary anticipation time and its application to long-term prediction of chaotic states

On Inverse Generalized Synchronization of Continuous Chaotic Dynamical Systems

“…and (18) and (19) Using simple calculations, we can show that (K − A) T + (K − A) is a positive definite matrix. Therefore, in this case, systems (18) and (19) are inverse generalized synchronized.…”

“…Therefore, in this case, systems (18) and (19) are inverse generalized synchronized. The error functions evolution is shown in Fig.…”

“…Complete synchronization [11,15], phase synchronization [17], lag synchronization [18], anticipated synchronization [19] of chaotic systems have been described theoretically and observed experimentally. Complete synchronization which is defined as the coincidence of states of interacting systems; phase synchronization which means entrainment of phases of chaotic oscillators, whereas their amplitudes remain uncorrelated; lag synchronization which appears as a coincidence of time-shifted states of two systems; and anticipated synchronization also appears as a coincidence of shifted-in-time states of two coupled systems, but in this case, in contrast to lag synchronization, the driven system anticipates the driver.…”

Research on the Expected Synchronization of Autonomous System

“…In general, most of the chaotic systems meet these conditions [12]. Consider the following two intercoupling systems: We know that if the origin of the error system (6) is asymptotically stable, the equation Based on the premise theory, similar to the Theorem 1 in [12], we can derive the sufficient condition, which can ensure that the origin of error system (6) is asymptotically stable. It must be pointed out that, there are little errors for the proof process of the sufficient condition.…”

“…In this method, the response system can keep synchronization with the future state of drive system, which was the response system predicting the future state of the drive system. The method was affirmed by the people, but in further study, the researchers found that there were some limitations in this method [12][13], in which the expected synchronization of Voss method is only suitable for continuous chaos systems with delay, and has some constraints on the expected time with the coupling coefficiency. To solve the limitations of Voss, the 12th literature proposed a method of Coupled bidirectional delay, and a sufficient condition theoretical framework based on Krasovskill-Lyapunov for the independence of delay, by which the expected synchronization of the system was researched in numerical simulation, a fractional order Rossler system as an example.…”