Multiple Mittag-Leffler stability and locally asymptotical ω-periodicity for fractional-order neural networks

Fractional calculus is a generalization of the conventional calculus. To describe the characteristic of the neural activity more veritably, fractional calculus is applied increasingly widely in the engineering fields. This paper presents theoretical results on the multiple Mittag-Leffler stability and locally S-asymptotical ω-periodicity for a general class of fractional-order neural networks. Several conditions are obtained to guarantee the invariance and boundedness of the solutions for this class of neural networks. By constructing appropriate Lyapunov functions, the multiple Mittag-Leffler stability is addressed. Furthermore, locally S-asymptotical ω-periodicity is discussed by reduction to absurdity and the final-value theorem. Some numerical examples with simulations are elaborated to showcase the effectiveness and validity of the obtained criteria.