Synchronization of Discrete-Time Fractional-Order Complex-Valued Neural Networks with Distributed Delays

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete Mittag-Leffler functions. In order to guarantee the global asymptotic stability, adequate criteria are determined using Lyapunov's direct technique, the Lyapunov approach, and some novel analysis techniques of fractional calculation. Thus, some sufficient conditions are obtained to guarantee the global stability. The validity of the theoretical results are finally shown using numerical examples.

Automated summary

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions for stability of the proposed networks are established using discrete fractional calculus, discrete Laplace transform, and fractional-order discrete Mittag-Leffler functions. Adequate criteria for global asymptotic stability are determined using Lyapunov's direct technique, Lyapunov approach, and novel analysis techniques of fractional calculation. Some sufficient conditions are obtained to guarantee global stability. The theoretical results are demonstrated using numerical examples.