Stability And Stabilization Of Two Kinds Of Fractional Order Neural Networks With Time Delays

Fractional order neural networks can describe some actual systems more accurately.In the real world,time delay is always inevitable,and it also causes some undesirable phenomena such as oscillation,bifurcation and instability to the system.We know that as a typical dynamic behavior,stability has been paid much attention by the authors.Therefore,it is of great theoretical significance to explore the stability of fractional order neural networks with time delays.In this paper,we investigate the stability of two kinds of fractional order neural networks with time delay which are stated as follows:In the second chapter,we investigates the finite-time stability for a class of fractional-order neural networks with proportional delay.Firstly,by some analytic techniques,a generalized Gronwall integral inequality with proportional delay is established.Based on this new inequality,a criterion is derived to guarantee the finite-time stability of systems when the fractional order is between 1 and 2.Moreover,when the fractional order is between 0 and 1,a new criterion is developed to ensure the finite-time stability of systems.This criterion is experimentally proved to be less conservative than those in the previous works.Finally,the effectiveness of our criteria is supported by some numerical examples.In the third chapter,we focuses on the stabilization problem for a class of fractional-order bidirectional associative memory neural networks with mixed time delays(discrete delay and finite-time distributed delay).Based on adaptive control and delay feedback control,two kinds of adaptive control schemes are proposed to realize the global stabilization of systems.Different from those in earlier works,our method mainly depends on two fractional inequalities and a new fractional-order Barbalat lemma.Finally,some numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed adaptive control schemes.