Multiple asymptotical stability analysis for fractional-order neural networks with time delays

Abstract

This paper formulates the multiple asymptotical stability for a general class of fractional-order neural networks with time delays. By exploiting the properties of upper bounded and lower bounded functions derived from the addressed fractional-order neural network model as well as the comparison principle for fractional-order calculus, a lot of sufficient conditions are obtained to guarantee the existence and multiple asymptotical stability of the equilibrium points for the fractional-order neural networks with time delays. It reveals that the results gained in this paper are applicable to analyses of both multiple asymptotical stability and global asymptotical stability. Besides, three numerical examples are presented to showcase the validity of the derived results.