| Fractional order BAM neural network is a kind of important model.It has the ability of bidirectional associative and infinite memory,and is widely applied in pattern recognition,signal processing and other fields.Compared with integer order model,fractional order model is more effective to accurately describe the complex natural phenomena.Therefore,it is more significant to research dynamic behaviors of fractional order systems.In order to broaden the application scope of fractional order systems,many scholars have analyzed corresponding controlled systems,regulating the convergence or bifurcation point by feedback control,which has become an important research topic.In this paper,fractional order BAM neural network model with linear feedback control is studied.It is divided into three parts: The first part mainly studies the existence and uniqueness of zero equilibrium point for neural network with linear feedback control;The second part investigates global Mittag-Leffler stability of the network with linear feedback control;The third part mainly analyzes the Hopf bifurcation of two classes of three dimensional time-delay fractional order BAM neural networks.Firstly,the existence and uniqueness of zero equilibrium point for fractional order BAM neural network with linear feedback control is proved using the principle of compression mapping and the Lipschitz conditions.Secondly,a lemma is given based on the Basic inequality.Using the lemma and generalized Gronwall-like inequality,we construct suitable Lyapunov functions to study global Mittag-Leffler stability of the network with linear feedback control.At the same time,several sufficient conditions are given,and numerical experiments verify the correctness of conditions.Finally,asymptotic stability and Hopf bifurcation of two classes of three dimensional time-delay fractional BAM neural networks are analyzed.According to numerical experiments,we show the effect of linear time delay feedback control on the bifurcation point. |
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