Stabilities And Applications Analysis Of Fractional-order Quaternion-valued Neural Networks

In the era of intelligent,artificial intelligence has become a key technology leading the new generation of scientific and technological revolution as well as industrial transformation.As the cornerstone of artificial intelligence,artificial neural network plays an important role in autonomous driving,speech and image recognition,optimization computing and other intelligent fields.In recent years,with the growth of data dimensions and the improvement of computing power,neural networks based on fractional calculus and quaternion have attracted great attention among various fields.In this thesis,stability of fractional-order quaternion-valued neural network and its application in image processing are studied.Thesis consists of six chapters.To begin with,the research background,significance and status quo are analyzed,and the research challenges are pointed out,the research contents,routes and methods are summarized as well.Then,the basic knowledge used in the research work are sorted out,including the definitions and lemmas of quaternion algebra,fractional calculus,and different mathematical models of neural networks.Besides,theoretical analysis that include the stability and synchronization discussion on two fractional-order quaternion-valued neural networks are conveyed.Moreover,the image processing method based on the stability and synchronization mechanism of fractional-order quaternion-valued neural network are presented.Finally,several innovative works of this research are concluded,and the further improvement direction of this research is discussed.In terms of theoretical analysis,a fractional-order quaternion-valued bidirectional associative memory neural network model with proportional delay and impulses is constructed firstly,which provides a feasible path from integer-order model to fractional-order system.By means of homeomorphic mapping theory,Lyapunov function and quaternion inequality technique,the unique existence and global exponential stability of the equilibrium point are discussed,and corresponding sufficient criteria are derived.Besides,the fractional-order quaternion-valued memristor neural networks with leakage delay and time-varying delays are considered with compared analysis between continuous-time and discrete-time cases.Based on Lyapunov functional and several fractional-order calculus inequalities,the sufficient conditions for global Mittag-Leffler synchronization of the driving-response system of fractional-order quaternion-valued memristive neural network are explored in continuous-time case.According to differential inclusion theory,Lyapunov method as well as Razumikhin condition,and by designing proper control protocol,sufficient but succinct criterion about the global ultimate Mittag-Leffler lag quasisynchronization of fractional-order quaternion-valued memristive neural networks is obtained in discrete-time case.As to the study on application,to begin with,the method of representing colored image by quaternion in single channel is introduced.Moreover,a face recognition method based on the stability of fractional-order quaternion-valued bidirectional associative memory is discussed.The network weight selection method based on fractional singular value decomposition and Lyapunov theory is proposed,and detailed steps to retrieve complete face image with corresponding information from noise image are given.In addition,a colored image encryption-decryption model based on the synchronized mechanism of one fractional-order quaternion-valued memristive neural networks is constructed,which provides a new thought to realize colored image encryption,and presents a novel encryptiondecryption working mechanism by the driver-response system.