Finite-time Stability Analysis Of Two Classes Of Fractional-order Neural Networks

As a typical dynamic behavior of complex systems,the research on stability is very important in theoretical research and practical application.In this paper,we study the finite-time stability for two classes of fractional-order neural networks with the order lying in the interval(1,2).Firstly,we investigate the finite-time stabilization of fractional-order delayed bidirectional associative memory neural networks.Based on feedback control,a sufficient condition is derived to realize the finite-time stabilization of systems by using the Cauchy-Schwartz inequality and the generalized Gronwall inequality.Meanwhile,two sufficient conditions are given to realize the finite-time stabilization of systems via partial feedback control.These conditions can be expressed as some simple algebraic inequalities,so they can be easily calculated in theoretical and practical applications.Finally,some numerical examples are provided to present the effectiveness of our results.Secondly,we investigate the finite-time stability of fractional-order Cohen-Grossberg neural networks with time delay.The existence and uniqueness of the equilibrium point are proved by the contraction mapping theorem,and the sufficient condition for finite-time stability are obtained by using the generalized Gronwall inequality and some elementary inequalities.The forms of these conditions are simple,so they can be easily calculated in theoretical research and practical applications.In addition,a sufficient condition is given to guarantee the finite-time stabilization of fractional-order delayed Cohen-Grossberg neural networks based on feedback control.Finally,some numerical simulations are presented to verify the correctness and effectiveness of theoretical results.