Abstract
In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme.
Highlights
Chaos is an interesting nonlinear phenomenon and has been known for a rather long time in the mathematics, physics, engineering and other related fields [5]
Motivated by the above discussion, synchronization of nonlinear dynamical systems with time-varying delays is investigated via a novel and generalized adaptive intermittent control protocol
The third one is that by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols
Summary
Chaos is an interesting nonlinear phenomenon and has been known for a rather long time in the mathematics, physics, engineering and other related fields [5]. For the real applications and the theoretical analysis, it is momentous to consider the synchronization problem of chaotic systems under aperiodically intermittent control scheme. Pinning synchronization of complex directed dynamical networks under decentralized adaptive strategy for aperiodically intermittent control was investigated in [28]. To the best of our knowledge, the synchronization problem for delayed dynamical systems under intermittent adaptive control, until now, receives few attentions. Motivated by the above discussion, synchronization of nonlinear dynamical systems with time-varying delays is investigated via a novel and generalized adaptive intermittent control protocol. The third one is that by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols.
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