Study On The Existence And Stability Of Anti-periodic And Almost Periodic Solutions Of Several Kinds Of Neural Networks

Artificial neural networks are proposed to imitate human brain neural function.They have high parallelism,high-speed information processing ability,super self-organization and self-learning ability.These excellent characteristics make them become the key research object of artificial intelligence.In addition,neural networks also have fault tolerance and strong function approximation ability,they have been successfully applied to pattern recognition,image processing,associative memory,optimal combination,signal processing,intelligent robot and other fields.Especially in the past decade,there are more and more journals and conferences related to neural networks.Neural network has become an interdisciplinary subject for joint discussion in mathematical science,control science,information science and other fields.In this thesis,based on continuation theorem of coincidence degree theory,Banach fixed point theorem,Lebesgue dominated convergence theorem,Wirtinger inequality,Lyapunov functional,analysis technique and proof by contradiction,we study the dynamical behaviors of quaternion-valued neural networks and Clifford-valued neural networks with various delays in detail,including the existence,uniqueness and global exponential stability of anti-periodic solutions,?-pseudo almost periodic solutions and(?,?)-pseudo almost automorphic solutions.In addition,as a special case of quaternion-valued and Clifford-valued neural networks,a class of generalized inertial shunting inhibitory cellular neural networks with distributed delays are also proposed in this thesis,and their dynamic characteristics are discussed.The specific work of this thesis is as follows:(i)We propose and prove the existence and global exponential stability of antiperiodic solutions of a class of generalized inertial shunting inhibitory cellular neural networks with distributed delays.In previous studies,the first derivative terms of inertial shunting inhibitory cellular neural networks are linear and their coefficients are constants.In chapter 3,we further generalize this model so that the first derivative terms can be nonlinear and the coefficients of the first derivative terms can be time-varying.(ii)We research the existence and global exponential stability of anti-periodic solutions of quaternion-valued shunting inhibitory cellular neural networks with distributed delays and impulses.(iii)We propose and prove the existence and global exponential stability of the antiperiodic solution of a class of inertial quaternion-valued high-order Hopfield neural networks with state-dependent delays.In previous studies,the coefficients of the first derivative terms and connection terms are constants.Considering that the coefficients of the real systems change with the environment.Therefore,we assume that all the parameters in the networks are time-varying.Without decomposing the quaternion-valued neural networks into real-valued or complex-valued neural networks,based on a continuation theorem of coincidence degree theory and the Wirtinger inequality,the existence of anti-periodic solutions of the networks is established.By constructing a suitable Lyapunov function,the global exponential stability of anti-periodic solutions of the networks is obtained.(iv)We obtain the existence and global exponential stability of anti-periodic solutions of a class of Clifford-valued high-order Hopfield neural networks with state-dependent delays and leakage delays.(v)We investigate the existence and global exponential stability of ?-pseudo almost periodic solutions of a class of Clifford-valued neutral neural networks with delays in the leakage term.Using a direct method,that is,without decomposing the Clifford-valued system under consideration into a real-valued system,we obtain sufficient conditions for the existence and global exponential stability of ?-pseudo almost periodic solutions of the Clifford-valued neural network under consideration.Our results are new even when the Clifford-valued system degenerates into a quaternion-valued system.(vi)We discuss the existence and global exponential stability of(?,?)-pseudo almost automorphic solutions of a class of Clifford-valued neural networks with infinitely distributed delays.Using a direct method,that is,without decomposing the Clifford-valued system under consideration into a real-valued system.Our results are new even when the Clifford-valued system degenerates into a quaternion-valued system.Our results are brand new.At the same time,our methods can be used to study the corresponding problems of other types of neural network systems.Some numerical examples are given to illustrate the feasibility of our results.