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This paper is concerned with the finite-time synchronization (FTS) of memristor-based recurrent neural networks (MRNNs) combined with inertial items and mixed delays, where both the discrete delays and bounded distributed delays are included. First, MRNNs with inertial items are of second-order state derivatives, thereby differing from the classical first-order MRNNs and bringing difficulties to study the dynamics of such systems. By using the order-reduction method, such kind of second-order MRNNs is transferred into conventional first-order differential systems. Then, under two kinds of designed feedback controllers, several sufficient conditions are derived ensuring the FTS of MRNNs with inertial items and mixed delays. Finally, numerical simulations are provided to show the effectiveness of the results and one application is also presented in pseudorandom number generation. [ABSTRACT FROM AUTHOR]

The existing results of passivity for neural networks mainly concentrated on first-order derivative of the states, whereas it is also significant to study the passivity with high-order derivative. In this paper, a class of memristor-based inertial neural networks (MINNs) with external inputs and outputs are concerned. First, by choosing appropriate variable transformation, the original networks are rewritten as first-order differential equations. Then a criterion of passivity for the MINNs is presented by nonsmooth analysis and linear matrix inequality (LMI) techniques, which could also result in NP-hard problem since it needs at least exponential-time to solve the passivity condition. Meanwhile, based on the obtained passivity criterion, asymptotic stability criterion is accordingly derived for MINNs. In order to avoid the NP-hard problem, we employ matrix-analysis-techniques with the property that the difference-matrix between the given matrix and the proposed matrix is seminegative definite. Then the time complexity for solving the proposed passivity criterion is reduced to constant-time with respect to the number of LMIs. Robust passivity for MINNs is also studied for bounded uncertain parameters. The MINN widens the application ranges for designing neural networks. Finally, relevant simulation examples are given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]