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The synchronization of complex networks, as an important and captivating dynamic phenomenon, has been investigated across diverse domains ranging from social activities to ecosystems and power systems. Furthermore, the synchronization of networks proves instrumental in solving engineering quandaries, such as cryptography and image encryption. And finite-time synchronization (FTS) controls exhibit substantial resistance to interference, accelerating network convergence speed and heightening control efficiency. In this paper, finite-time synchronization (FTS) is investigated for a class of fractional-order nonidentical complex networks under uncertain parameters (FONCNUPs). Firstly, some new FTS criteria for FONCNUPs are proposed based on Lyapunov theory and fractional calculus theory. Then, the new controller is designed based on inequality theory. Compared to the general controller, it controls all nodes and adds additional control to some of them. When compared to other controllers, it has lower control costs and higher efficiency. Finally, a numerical example is presented to validate the effectiveness and rationality of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic and pinning synchronization of fractional-order nonidentical complex dynamical networks with uncertain parameters (FONCDNUP). First of all, some synchronization criteria of FONCDNUP are proposed by using the stability of fractional-order dynamical systems and inequality theory. Moreover, a novel controller is derived by using the Lyapunov direct method and the differential inclusion theory. Next, based on the Lyapunov stability theory and pinning control techniques, a new group of sufficient conditions to assure the synchronization for FONCDNUP are obtained by adding controllers to the sub-nodes of networks. At last, two numerical simulations are utilized to illustrate the validity and rationality of the acquired results. [ABSTRACT FROM AUTHOR]

In this paper, the fixed-time multi-switch combination–combination synchronization (FTMSCCS) of fractional-order chaotic systems with uncertainties and external disturbances is studied. The appropriate sliding mode surface and controller are proposed based on a Lyapunov theorem, and fixed-time multi-switching combination–combination synchronizations between four fractional-order chaotic systems are realized. The Lyapunov function is designed to prove the feasibility of the controller theoretically, and the effectiveness and robustness of the synchronization mechanism are further verified by numerical simulations. The advantage of this article is that it extends fixed-time synchronization to multi-switch combination–combination synchronization, enabling synchronization for a limited time, while increasing the complexity of the synchronization mechanism and improving its confidentiality in communication applications. [ABSTRACT FROM AUTHOR]

This paper deals with the asymptotic synchronization of fractional-order complex dynamical networks with different structures and parameter uncertainties (FCDNDP). Firstly, the FCDNDP model is proposed by the Riemann–Liouville (R-L) fractional derivative. According to the property of fractional calculus and the Lyapunov direct method, an original controller is proposed to achieve the asymptotic synchronization of FCDNDP. Our controller is more adaptable and effective than those in other literature. Secondly, a sufficient condition is given for the asymptotic synchronization of FCDNDP based on the asymptotic stability theorem and the matrix inequality technique. Finally, the numerical simulations verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]