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This paper is dedicated to addressing the issue of the finite-time synchronization of complexed-valued neural networks with finite-time distributed delays. Some results are derived for finite-time synchronization of the drive-response system using the new Lyapunov–Krasovskii function and the analysis techniques. We then propose several numerical examples to determine the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a finite-time lag synchronization of coupled neural networks with time delay is investigated. By means of the Lyapunov stability theory, a feedback controller is designed for achieving lag synchronization between two delayed neural networks systems in finite time. Paper extends some basic results from the area of finite time to time-delay systems. Numerical simulations on coupled Lu neural systems illustrate the effectiveness of the results. [Copyright &y& Elsevier]

This paper investigates the mechanisms of small parametrical perturbations in controlling chaos in a class of non-autonomous piecewise smooth oscillators, which describe a large class of nonlinear dynamical systems in the real world. The analytical expressions of two homoclinic orbits of unperturbed piecewise smooth oscillators, which connect the same hyperbolic saddle point are solved analytically. Firstly, when there are no small parametrical perturbations, by using Melnikov׳s approach, it is rigorously proven that the homoclinic chaos in the Smale horseshoes sense exists when the system׳s parameters are selected above the threshold for chaos occurrence. Secondly, under the small parametrical perturbations, by using Melnikov׳s approach, a sufficient criterion is derived, serving as designing the parameters of the control signal, i.e., amplitude and phase position. In the process of computing Melnikov׳s functions, it is found that the expressions of Melnikov׳s functions could not be solved analytically because the homoclinic orbits are highly complicated. To this end, a numerical algorithm is proposed. Numerical simulations are presented to verify the theoretical results. The results of this paper can be used to explore the underlying chaotic behaviors of the inertial neural network model. [ABSTRACT FROM AUTHOR]

In this paper, an ideal current source forgetting memristor model is proposed. Based on the model, three kinds of synapses with long- and short-term memory are designed: the series forgetting memristor synapse, the forgetting memristor bridge synapse written independently and the forgetting memristor bridge synapse written in batches. Combined with the forgetting property, the long- and short-term weight of the forgetting synapse can be controlled by the long- and short-term resistance of memristors. Compared the three forgetting synapses, the series forgetting memristor synapse has the lowest requirement for memristors, the forgetting memristor bridge synapse written independently is the most flexible, and the forgetting memristor bridge synapse written in batches is the most convenient. Compared with traditional synapses, forgetting synapses with long- and short-term memory have multi-weight storage. When forgetting synapses are applied to associative memory, it can be found more patterns are stored in the neural network and different patterns are recalled at different time due to the forgetting effect. [ABSTRACT FROM AUTHOR]

This paper focuses on the hybrid effects of coupling, time-varying delay, intermittent controller on memristor-based neural networks. Firstly, we constructed an array of linearly coupled memristor-based neural networks with time-varying delay. Secondly, our sufficient conditions, ensuring the stability and synchronization, are dependent on coupling and intermittent control and show coupling and intermittent control on the stability and synchronization of memristor-based neural networks. Finally, numerical simulations were given to verify the theoretical results. [ABSTRACT FROM AUTHOR]