Synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights and discontinuous nodes based on sliding mode control strategy

Quasi-synchronization for variable-order fractional complex dynamical networks with hybrid delay-dependent impulses

This paper focuses on addressing the problem of quasi-synchronization in heterogeneous variable-order fractional complex dynamical networks (VFCDNs) with hybrid delay-dependent impulses. Firstly, a mathematics model of VFCDNs with short memory is established under multi-weighted networks and mismatched parameters, which is more diverse and practical. Secondly, under the framework of variable-order fractional derivative, a novel fractional differential inequality has been proposed to handle the issue of quasi-synchronization with hybrid delay-dependent impulses. Additionally, the quasi-synchronization criterion for VFCDNs is developed using differential inclusion theory and Lyapunov method. Finally, the practicality and feasibility of this theoretical analysis are demonstrated through numerical examples.

Disturbance rejection for multi-weighted complex dynamical networks with actuator saturation and deception attacks via hybrid-triggered mechanism

In this work, we address hybrid-driven-based robust synchronization problem for multi-weighted complex dynamical networks with actuator saturation and deception attacks. The hybrid-triggered mechanism, which combines a switch between the event-triggered scheme and the time-triggered scheme, is often used to reduce the data transmission and the alleviate network burden. Further, the equivalent-input-disturbance technique is applied to eliminate the unknown disturbance effect of the addressed system. Moreover, a memory controller is designed under actuator saturation to ensure that the resultant augmented system is asymptotically synchronized even in the presence of deception attacks. Finally, three numerical examples are given to show the validity of the obtained theoretical results.

New finite-time synchronization conditions of delayed multinonidentical coupled complex dynamical networks

In this article, we mainly focus on the finite-time synchronization of delayed multinonidentical coupled complex dynamical networks. By applying the Zero-point theorem, novel differential inequalities, and designing three novel controllers, we obtain three new criteria to assure the finite-time synchronization between the drive system and the response system. The inequalities occurred in this paper are absolutely different from those in other papers. And the controllers provided here are fully novel. We also illustrate the theoretical results through some examples.

Exponential Synchronization of Hyperbolic Complex Spatio-Temporal Networks with Multi-Weights

This paper deals with the leader-following synchronization of first-order, semi-linear, complex spatio-temporal networks. Firstly, two sorts of complex spatio-temporal networks based on hyperbolic partial differential equations (CSTNHPDEs) are built: one with a single weight and the other with multi-weights. Then, a new distributed controller is designed to address CSTNHPDE with a single weight. Sufficient conditions for the synchronization and exponential synchronization of CSTNHPDE are presented by showing the gain ranges. Thirdly, the proposed distributed controller addresses of CSTNHPDE with multi-weights, and gain ranges are obtained for synchronization and exponential synchronization, respectively. Finally, two examples show the effectiveness and good performance of the control methods.

Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays

In this article, we discuss bipartite fixed-time synchronization for fractional-order signed neural networks with discontinuous activation patterns. The Filippov multi-map is used to convert the fixed-time stability of the fractional-order general solution into the zero solution of the fractional-order differential inclusions. On the Caputo fractional-order derivative, Lyapunov-Krasovskii functional is proved to possess the indefinite fractional derivatives for fixed-time stability of fragmentary discontinuous systems. Furthermore, the fixed-time stability of the fractional-order discontinuous system is achieved as well as an estimate of the new settling time.. The discontinuous controller is designed for the delayed fractional-order discontinuous signed neural networks with antagonistic interactions and new conditions for permanent fixed-time synchronization of these networks with antagonistic interactions are also provided, as well as the settling time for permanent fixed-time synchronization. Two numerical simulation results are presented to demonstrate the effectiveness of the main results.