Abstract
This paper investigates modified function projective synchronization (MFPS) for complex dynamical networks with mixed time-varying and hybrid asymmetric coupling delays, which is composed of state coupling, time-varying delay coupling and distributed time-varying delay coupling. In contrast to previous results, the coupling configuration matrix needs not be symmetric or irreducible. The MFPS of delayed complex dynamical networks is considered via either hybrid control or hybrid pinning control with nonlinear and adaptive linear feedback control, which contains error linear term, time-varying delay error linear term and distributed time-varying delay error linear term. Based on Lyapunov stability theory, adaptive control technique, the parameter update law and the technique of dealing with some integral terms, we will show that control may be used to manipulate the scaling functions matrix such that the drive system and response networks could be synchronized up to the desired scaling function matrix. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results in this article generalize and improve the corresponding results of the recent works.
Highlights
Complex networks, as an interesting subject, have been thoroughly investigated for decades
Remark In Theorem . , we investigated the modified function projective synchronization (MFPS) of complex dynamical networks via hybrid control, where the control ui (t) is a nonlinear control to apply for every node
Remark If we investigate the dynamical nodes without delays and ignore the adaptive linear feedback control, which contains time-varying delay error linear term and distributed time-varying delay error linear term, we can see the general model of the complex dynamical networks in [, ]
Summary
As an interesting subject, have been thoroughly investigated for decades. Section presents MFPS of the complex dynamical network with mixed time-varying delay and hybrid asymmetric coupling by hybrid adaptive control and hybrid adaptive pinning control, respectively.
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