Stability Analysis Of Several Classes Of Quaternion-Valued Cohen-Grossberg Neural Networks

Both quaternion-valued neural networks and Cohen-Grossberg(C-G)neural networks have a wide range of applications in image processing,color recognition,3D spatial modeling,optimization,control and other fields.And quaternion-valued neural networks can be seen as an extension of quaternion algebraic theory,which is obtained by modifying the parameters of states,connection weights and activation functions,all of which are in the quaternion domain.The quaternion-valued C-G neural network is also obtained by modifying the parameters of the C-G neural network to quaternion values.Therefore,quaternion-valued C-G neural networks can be regarded as an extension of quaternion-algebraic theory to C-G neural networks.In this paper,we analyze and study several types of quaternion-valued C-G neural network stability problems.The contents are as follows.In Chapter 1,we presents an overview of the development of quaternion-valued neural networks and C-G neural networks.In Chapter 2,the existence uniqueness and exponential stability of the equilibrium point of quaternion-valued C-G neural network are obtained by using M-matrix theory,homogeneous mapping principle,and vectorial Lyapunov function method to study the quaternion-valued CG neural network system with non-differentiable time lag.Finally,the validity and correctness of the conclusions are verified by numerical simulation experiments.In Chapter 3,the existence,uniqueness and stability of equilibrium points of quaternionvalued neutral C-G neural network with variable time lag are investigated.The system is taken as a whole,the existence of unique equilibrium point is deduced by homogeneous mapping theorem,inequality and linear matrix inequality(LMI),and the sufficient conditions for the global asymptotic stability of the equilibrium point are derived by constructing a suitable Lyapunov function,and the obtained results can be checked by using the YALMIP toolbox in MATLAB.Finally,the validity and correctness of the obtained results are proved by two numerical examples.