Multistability Analysis For Several Classes Of Fractional-order Neural Networks

In recent years,some valuable results have been obtained about multistability of neural net-works.However,it is worth pointing out that most existing multistability results are derived under the assumption that the considered neural networks models are classical integer-order models.Frac-tional calculus has more advantages than integer-order calculus in describing neurons with memory and hereditary properties.Based on the theory of fractional-order differential equation,the fixed point theorem,the Lyapunov functional method and comparison principle,this dissertation discuss-es the multistability for several classes of fractional-order neural networks,including fractional-order competitive neural networks and fractional-order delayed Hopfield neural networks.This dissertation is divided into four chapters and the main contents are summarized as follows.In the first chapter,the current research situations are briefed,which concern multistability of integer-order neural networks and dynamical analysis of fractional-order neural networks.The main contents and the main contributions of this dissertation are also expounded according to the above-mentioned analysis.In the second chapter,we investigate the coexistence and dynamical behaviors of multiple equi-librium points for fractional-order competitive neural networks with Gaussian activation functions.By virtue of the geometrical properties of activation functions,the fixed point theorem and the the-ory of fractional-order differential equation,some sufficient conditions are established to guarantee that such n-neuron neural networks have exactly 3~kequilibrium points with 0?k?n,among which 2~k(0?k?n)equilibrium points are locally Mittag-Leffler stable.The obtained results cover both multistability and mono-stability of fractional-order neural networks and integer-order neural networks.Two illustrative examples with their computer simulations are presented to verify the theoretical analysis.In the third chapter,we discuss the multistability of fractional-order Hopfield neural networks with Gaussian activation functions and multiple time delays.By using the geometrical properties of activation functions,the fixed point theorem,the theory of fractional-order differential equation,the Lyapunov functional method and comparison principle,we present some sufficient conditions to ensure such n-neuron neural networks can have exactly 3~nequilibrium points,among them2~nequilibrium points are locally asymptotically stable.Two examples are provided to show the effectiveness of the theoretical results.In the last chapter,the research work of this dissertation is summarized.Furthermore,the possible improved methods are proposed and the prospect for the future work is made.