Abstract
The problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for delayed dynamic complex networks via developing control schemes is concerned. First, by comparing with the existing results, some new results for delayed networks model to ensure the synchronization of FXT and PAT are obtained. Second, some looser conditions are obtained for FXT synchronization, and several more accurate settling time (ST) estimates are established through several special functions. Third, by using some non-trivial control strategy, the PAT synchronization is investigated with limited control gains, and the synchronization time is able to specified in advance on the basis of practical need and is not relate to any parameter and any initial value. In particular, as a distinct form, the essential conditions for the FXT and PAT synchronization are obtained for the coupled neural networks. last, the improved the FXT and PAT synchronization results of dynamic delayed networks are demonstrated by one numerical example.
Highlights
Complex networks are complex aggregates composed of interrelated and interactive basic units with certain characteristics and functions
In this essay, the FXT and PAT synchronization are investigated for a type coupled system with delay
The established conditions are more relaxed in this paper and comparison with the existing results, the values for settling time (ST) are more precise
Summary
Complex networks are complex aggregates composed of interrelated and interactive basic units (nodes) with certain characteristics and functions. Liu et al considered PAT synchronization problem of coupled networks via continuous activation function by designing delayed and unbounded control strategy in [24]. Based on the above discussion, the problem of FXT and PAT synchronization for delayed dynamic complex networks via developing control schemes is concerned. For the sake of making the states of system (3) FXT or PAT synchronize with z(t), controlled delayed system is given in the following. In [24], by proposing an unbounded and time varying control strategy, Liu studied cluster synchronization with a PAT of complex networks. Using Lemmas 3-5, the network can realize fixed-time synchronization under linear feedback control in this paper. It is meaningful to concern this problem in our recent research topics
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