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Summary: This paper solves the finite‐time synchronization and adaptive synchronization problems of drive‐response memristive recurrent neural networks with delays under two control methods. First, the state‐feedback control rule containing delays and the adaptive control rule are designed for realizing synchronization of drive‐response memristive recurrent neural networks in finite time. Then, on the basis of the Lyapunov stability theory, many algebraic sufficient conditions are obtained to guarantee finite‐time synchronization and adaptive synchronization of drive‐response memristive recurrent neural networks via two control methods, which are easily verified. In addition, the estimation of the upper bounds of the settling time of finite‐time synchronization is obtained. Lastly, to illustrate the effectiveness of the obtained theoretical results, two examples are given. [ABSTRACT FROM AUTHOR]

Two-dimensional gyroscopic torque can be produced by tilting the rotor shaft of the active magnetically suspended momentum wheel. The nonlinear magnetic torque is analyzed and then an adaptive back-stepping tracking method is proposed to deal with the nonlinearity and uncertainty. The nonlinearity of magnetic torque is represented as bounded unknown uncertainty stiffness, and an adaptive law is proposed to estimate the stiffness. Combined with back-stepping method, the proposed method can deal with the uncertainty. This method is designed by Lyapunov stability theory to ensure the stability, and its effectiveness is validated by simulations and experiments. These results indicate that this method can realize higher tracking precision and faster tracking velocity than the conventional cross feedback method to provide high precision and wide bandwidth outputting torque. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the synchronization and parameter identification of chaotic system with unknown parameters and mixed delays. A new approach is proposed for designing a controller and a update rule of unknown parameters based on a special matrix structure, and the synchronization and the parameter identification are realized under the controller and the update rule. Numerical simulations are carried out to confirm the effectiveness of the approach. A significant advantage is that the process of designing a controller and a update rule become very clear and easy by the proposed approach. [Copyright &y& Elsevier]

In this paper, the problem of adaptive synchronization for a class of stochastic neural networks (SNNs) which involve both mixed delays and Markovian jumping parameters is investigated. The mixed delays comprise the time-varying delays and distributed delays, both of which are mode-dependent. The stochastic perturbations are described in terms of Browian motion. By the adaptive feedback technique, several sufficient criteria have been proposed to ensure the synchronization of SNNs in mean square. Moreover, the proposed adaptive feedback scheme is applied to the secure communication. Finally, the corresponding simulation results are given to demonstrate the usefulness of the main results obtained. [ABSTRACT FROM AUTHOR]

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed time-varying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

Abstract: We indicate that the proof of theorem is incorrect in Letter [Y. Xu, W. Zhou, J. Fang, W. Sun, Phys. Lett. A 374 (2010) 1673]. For correcting the mistakes, a correct version of the proof of theorem is given in this Letter. [Copyright &y& Elsevier]