Finite-time mixed outer synchronization of complex networks with coupling time-varying delay

Finite-Time Synchronization and H∞ Synchronization for Coupled Neural Networks With Multistate or Multiderivative Couplings

This article investigates the finite-time synchronization (FTS) and H∞ synchronization for two types of coupled neural networks (CNNs), that is, the cases with multistate couplings and with multiderivative couplings. By designing appropriate state feedback controllers and parameter adjustment strategies, some FTS and finite-time H∞ synchronization criteria for CNNs with multistate couplings are derived. In addition, we further consider the FTS and finite-time H∞ synchronization problems for CNNs with multiderivative couplings by utilizing state feedback control approach and selecting suitable parameter adjustment schemes. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed criteria.

On Pinning Linear and Adaptive Synchronization of Multiple Fractional-Order Neural Networks With Unbounded Time-Varying Delays

In this article, the synchronization of multiple fractional-order neural networks with unbounded time-varying delays (FNNUDs) is investigated. By introducing a pinning linear control, sufficient conditions are provided for achieving the synchronization of multiple FNNUDs via an extended Halanay inequality. Moreover, a new effective adaptive control which applies to the fractional differential equations with unbounded time-varying delays is designed, under which sufficient criteria are presented to ensure the synchronization of multiple FNNUDs. The introduced control in this article is also workable in traditional integer-order neural networks. Finally, the validity of obtained results is demonstrated by a numerical example.

Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay

In this article, we investigate the synchronization of complex networks with general time-varying delay, especially with nondifferentiable delay. In the literature, the time-varying delay is usually assumed to be differentiable. This assumption is strict and not easy to verify in engineering. Until now, the synchronization of networks with nondifferentiable delay through adaptive control remains a challenging problem. By analyzing the boundedness of the adaptive control gain and extending the well-known Halanay inequality, we solve this problem and establish several synchronization criteria for networks under the centralized adaptive control and networks under the decentralized adaptive control. Particularly, the boundedness of the centralized adaptive control gain is theoretically proved. Numerical simulations are provided to verify the theoretical results.

UCFTS: A Unilateral Coupling Finite-Time Synchronization Scheme for Complex Networks

Improving universality and robustness of the control method is one of the most challenging problems in the field of complex networks (CNs) synchronization. In this paper, a special unilateral coupling finite-time synchronization (UCFTS) method for uncertain CNs is proposed for this challenging problem. Multiple influencing factors are considered, so that the proposed method can be applied to a variety of situations. First, two kinds of drive-response CNs with different sizes are introduced, each of which contains two types of nonidentical nodes and time-varying coupling delay. In addition, the node parameters and topological structure are unknown in drive network. Then, an effective UCFTS control technique is proposed to realize the synchronization of drive-response CNs and identify the unknown parameters and topological structure. Second, the UCFTS of uncertain CNs with four types of nonidentical nodes is further studied. Moreover, both the networks are of unknown parameters, time-varying coupling delay and uncertain topological structure. Through designing corresponding adaptive updating laws, the unknown parameters are estimated successfully and the weight of uncertain topology can be automatically adapted to the appropriate value with the proposed UCFTS. Finally, two experimental examples show the correctness of the proposed scheme. Furthermore, the method is compared with the other three synchronization methods, which shows that our method has a better control performance.

Globally fixed-time synchronization of coupled neutral-type neural network with mixed time-varying delays

This paper mainly studies the globally fixed-time synchronization of a class of coupled neutral-type neural networks with mixed time-varying delays via discontinuous feedback controllers. Compared with the traditional neutral-type neural network model, the model in this paper is more general. A class of general discontinuous feedback controllers are designed. With the help of the definition of fixed-time synchronization, the upper right-hand derivative and a defined simple Lyapunov function, some easily verifiable and extensible synchronization criteria are derived to guarantee the fixed-time synchronization between the drive and response systems. Finally, two numerical simulations are given to verify the correctness of the results.