Global synchronization for BAM delayed reaction-diffusion neural networks with fractional partial differential operator. Issue 1 (January 2023) - Wang, Chen; Zhang, Hai; Stamova, Ivanka; Cao, Jinde
Abstract: This paper is devoted to the exploration of the global asymptotic synchronization (GAS) and global Mittag–Leffler synchronization (GMLS) issues on bidirectional associative memory reaction-diffusion neural networks (BAMRDNNs), which include a Caputo's fractional partial differential operator, leakage and discrete delays. By means of the Green's theorem, Jensen's integral inequality and Lyapunov functional approach, several synchronization criteria are established by using the hybrid controllers. The presented results are described in the algebraic inequalities form, which can immensely reduce the computational complexity. Moreover, these results reveal the impact of the network system coefficient matrices on GAS and GMLS. Finally, in the three-dimensional space, the effectiveness and practicability of these synchronization criteria are confirmed by choosing different derivative orders and diffusion coefficients.