Qualitative Studied On Several Kinds Of Differential Equations With Discontinuous Right-Hand Sides

In this paper,the existence of asymptotically almost periodic solutions of quaternionvalued cellular neural networks with discontinuous activation function with time-varying and infinitely distributed delays and the fixed time synchronization of octonion-valued memristor neural networks with leakage delays and time-varying delays are studied.Firstly,the real and imaginary parts of the quaternion neural networks are decomposed and the equivalent differential equations are established.Based on differential inclusion,set-valued mapping,diagonally dominant rule and Lyapunov functional methods,the sufficient conditions for asymptotically almost periodic solutions of equivalent differential equations are obtained.Secondly,the real and imaginary parts of the quaternion-valued neural networks are decomposed and the equivalent differential equations are established.By means of differential inclusion,set-valued mapping,fixed time synchronization theory and Lyapunov functional methods,the sufficient conditions for fixed time synchronization of equivalent differential equations are obtained under a new nonlinear feedback state controller.Then,the validity of the results is verified by giving a numerical example.Finally,the conclusion of this paper is given.