Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations

This paper considers the drive-response synchronization in finite time of competitive neural networks (CNNs) with different time scales, time-varying and infinite-time distributed delays (mixed delays), as well as uncertain non-linear perturbations. The drive and response systems are disturbed by different uncertain non-linear perturbations. The effects of the non-identical uncertain non-linear perturbations are suppressed by designing some simple controllers. Moreover, by designing new Lyapunov-Krasovskii functionals, sufficient conditions are obtained to guarantee that the CNNs can be synchronized in a setting time without using existing finite-time stability theorem. Furthermore, the setting time is explicitly estimated for CNNs with bounded distributed delay and without delay. It is shown that the setting time is dependent on the time delays and the initial values of the coupled CNNs. Some results on synchronization of CNNs are essentially extended. Finally, numerical examples are provided to illustrate the effectiveness of the presented synchronization scheme.