Dynamics Behaviors Of Inertial Neural Networks And Quaternion-Valued Neural Networks

Neural networks are with their various intelligent properties such as powerful self-learning ability,high rate of fault tolerance,associative memory and so on.It has become the foundation of deep learning and the cornerstone of implement of artificial intelligence.And it is also the preferred method of data mining.Moreover,it has been successfully applied in pattern recognition,forecast estimate,and intelligent traffic,etc.Therefore,the research upsurges to neural networks have been launched again by scholars.The dynamics characteristics of quaternion-valued neural networks and inertial neural networks are discussed in this doctoral thesis.As a special case of quaternion-valued neural networks,the dynamics properties of complex-valued neural networks are also considered here.This thesis is divided into five main chapters.The dynamics characteristics of inertial neural networks are investigated in the second chapter.The stability in Lagrange sense of complex-valued neural networks is discussed in the third chapter.In the fourth chapter,the dynamics behaviors of quaternionvalued neural networks are explored.Conclusions of this thesis are summarized briefly in the fifth chapter.More details are listed as following:In Chapter 2,firstly,by introducing a suitable substitution,the inertial system is transformed to a first order differential system.With the help of Lyapunov functional,inequality techniques and analytical method,the Lagrange stability and Lagrange exponential stability of delayed inertial neural networks are studied.Secondly,by employing matrix measure,matrixnorm inequality,and generalized Halanay inequality,the global dissipativity for inertial neural networks with parameter uncertainties is discussed.Finally,by virtue of differential inclusion theory and analytical techniques,some sufficient criteria are established to ascertain the global dissipativity for delayed memristor-based inertial networks.In Chapter 3,by employing Lyapunov theory,generalized Halanay inequality,linear matrix inequality and matrix measure approach,the Lagrange stability of complex-valued neural networks is investigated.Firstly,the Lagrange stability of delayed complex-valued neural networks with two different classes of activation functions is discussed.The specific estimations of positive invariant set and globally attractive set are given out.Secondly,the Lagrange stability of complex-valued neural networks with neutral delay and different classes of activation functions is considered respectively.Complex-valued neural networks are equivalently divided into two real-valued neural networks,and then by virtue of analytic techniques and Lyapunov theory,some delay-dependent criteria are established to guarantee the aforementioned neural networks to be globally exponentially Lagrange stable.In Chapter 4,firstly,the fundamental theories of quaternion are reviewed,and then the quaternion-valued neural networks are equivalently transformed into four real-valued systems.The asymptotic stability and exponential stability are investigated via nonlinear measure approach.Moreover,compared to some existing results,the less conservativeness of the obtained results is also showed by two comparison examples.Secondly,the stability of quaternion-valued neural networks with mixed time delay is analyzed by Lyapunov theory along with linear matrix inequalities,and the obtained results can be checked by the LMI tool box in Matlab.Finally,the dissipativity of delayed quaternion-valued neural networks is discussed as a single entirety without decomposition.Based on Lyapunov theory and some analytic techniques,several algebraic criteria are provided to guarantee the quaternion-valued neural networks to be global dissipative and exponential dissipative.In Chapter 5,conclusions of this thesis are summarized briefly,and several subjects which deserve further study are given out.