Almost Periodic Solutions And Homoclinic And Heteroclinic Of Quaternion-valued Differential Equations

In this paper,we study the quaternion-valued inertial Cohen-Grossberg cellular neural networks with time-varying delays and quaternion-valued cellular neural networks with rectangular input currents and D operator.In chapter two,we study the global exponential almost periodic synchronization of quaternion-valued inertial C-G cellular neural networks with time-varying delays by direct method.Firstly,we use the Banach fixed point theorem to obtain the existence of almost periodic solutions of quaternion-valued inertial Cohen-Grossberg cellular neural networks with time-varying delays.Besides,by designing a general controller,using differential inequality techniques and constracting a suitable Lyapunov function,introduce some variable transformation and using the properties of the integral,two sufficient conditions are obtained to ensure the global exponential almost periodic synchronization for drive-response system,and complement each other.At the end of the paper,an example is given to verify the effectiveness of the obtained results.In the third chapter,the dynamics of a class of quaternion-valued cellular neural networks with rectangular input currents and D operator are studied by using the Banach fixed point theorem and the asymptotic viewpoint.Under certain conditions,we prove that such network has homoclinic and heteroclinic outputs.Finally,an numerica example is given to verify the feasibility of our main results.