Asymptotic Stability of Fractional-Order Incommensurate Neural Networks

The dynamics and stability of fractional-order (FO) neural networks (FONN) and FO memristive neural networks (FOMNN), have received great attention in the last years. However, most research focused merely on commensurate FONN (all neurons have the same order). This paper addresses the stability of a class of incommensurate FONN for the first time. Firstly, using the comparison principle for FO systems with multi-order, the stability of FO nonlinear systems with multi-order is treated similarly to the stability of incommensurate FO linear systems. Then, adopting the stability results of incommensurate FO linear systems, an asymptotic stability criterion for FONN is established. The proposed method is valid for investigating the stability and synchronization of uncertain FONN and FOMNN with multi-order. Numerical simulations illustrate the theoretical results and their effectiveness.