Stability Analysis Of Fractional-order Neural Networks

Fractional order neural network is an extension and deepening of the integer order neural network.It is more important for the complexity of the dynamical system and the accuracy of the description of the neuron.In this paper,based on fractional order Lyapunov stability theory and mathematical analysis method,we study the issue of the Mittag-Leffler stability and projective synchronization of the fractional-order neural networks with inverse Lipschitz neuron activations,the main contents are as follows:Firstly,an inequality for the Caputo derivative of compound function,with 0(27)?(27)1,is introduced,which plays the central role in the stability analysis.Based on topological degree theory and inequality techniques,the proof of the existence and uniqueness of the equilibrium point is presented.A sufficient condition ensuring the Mittag-Leffler stability of the network is given by constructing appropriate Lyapunov function.And two numerical examples are provided to illustrate the validity of the theoretical results obtained.Secondly,by using the fractional Lyapunov stability theorem,the issue of the global asymptotic synchronization of the fractional-order neural networks with inverse Lipschitz neuron activations is investigated on the basis of previous study.By choosing appropriate controller,using quadratic function and LMI method,a sufficient condition for projective synchronization is obtained,and then two numerical examples are given.Finally,a class of fractional-order neural networks with delays and inverse Lipschitz neuron activations is investigated.Based the fixed point principle,the proof of the existence and uniqueness of the equilibrium point is presented.A sufficient condition ensuring the uniform stability of the network is given by the methods of mathematical analysis.Finally,by choosing different initial values,two numerical examples are given to illustrate the validity of the theoretical results obtained.