Abstract
This paper is concerned with two-layer complex networks with unidirectional interlayer couplings, where the drive and response layer have time-varying coupling delay and different topological structures. An adaptive control scheme is proposed to investigate finite-time mixed interlayer synchronization (FMIS) of two-layer networks. Based on the Lyapunov stability theory, a criterion for realizing FMIS is derived. In addition, several sufficient conditions for realizing mixed interlayer synchronization are given. Finally, some numerical simulations are presented to verify the correctness and effectiveness of theoretical results. Meanwhile, the proposed adaptive control strategy is demonstrated to be nonfragile with the noise perturbation.
Highlights
As an important and typical dynamic behavior of complex networks, synchronization has been extensively investigated in many fields, such as physics, mathematics, information science, biology, and sociology
finite-time mixed interlayer synchronization (FMIS) is analyzed when the two-layer networks are disturbed by the additive noise
We will give some sufficient conditions for realizing FMIS or mixed interlayer synchronization (MIS) of two-layer networks based on adaptive control
Summary
As an important and typical dynamic behavior of complex networks, synchronization has been extensively investigated in many fields, such as physics, mathematics, information science, biology, and sociology. Interlayer synchronization is called counterpart synchronization [11] which describes how the nodes in one network behave coherently with the corresponding ones in other connected networks This concept can be regarded as the development of synchronization for coupled driveresponse systems [12]. Wang et al [22] studied MOS between two complex networks with the same topological structure and time-varying coupling delay by Advances in Mathematical Physics. In [25], He et al discussed FMOS between two complex networks with time-varying coupling delay and the same topological structures by designing a simple and robust linear state feedback controller. We consider FMIS of two-layer networks with time-varying coupling delay and different topological structures by designing an adaptive control scheme.
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