Studies Of Asymptotic Behaviors On Some Neural Networks With Time-varying Delays

Hopfield Neural Networks(CNN) model and its similar models(BAM,CNN) have found applications in different areas,such as image processing,pattern recognition and optimization etc.Theory analysis for those models is an important topic in the neural network fields.For both the natural systems and the social systems,stability of a system is firstly to consider.In the mean time,time delays exist in many systems and it results in additional difficulties in the analysis of the dynamical behaviors of systems.Base on a review of research status and general development situation of stability of Neural Networks above,an in-depth research on the dynamical behaviors on those models with time delays is made in this dissertation.Using a result of former Russia famous scholar Krasovski-Baribashin as lemma,a new theorem on global asymptotic stability of Hopfield neural networks have been obtained.Firstly the results improve activation function,which both can be sigmoid function and can be local Lipschitz function.Secondly the hypothesis about weight matrix is symmetric is not needed.Finally the primary condition of diagonal stability changes that of diagonal semi-stability.Thus the results generalize and improve the core theorem of stability on Hopfield neural networks.Diagonal stability is mainly method for stability on Hopfield neural networks,but a problem of the existence for diagonal positive matrix arises.Although M matrix condition is stronger than diagonal stability condition,the former is applied easily for its checking conveniently.By using Lyapunov function,the condition of M matrix on global asymptotic stability of Hopfield neural networks enlarge the condition of semi-M matrix. There are seldom papers about non-stability of Hopfield neural networks.An improved condition on non-stability of Hopfield neural networks is given.Using Razumikhin conditions,some stability conditions of Hopfield neural networks with time-varying delays are obtained.The results,including delay independent results and delay dependent results,generalize the corresponding conclusions existed.Delay dependent condition is for the model with delay-feedback items.The model with delays is the same stability as the primary model when delays are enough small.Delay independent condition is for the model with delay-feedback items and feedback items.The model with delays is asymptotic stable,whatever delays change,when coefficients satisfy the conditions given.Some results concerning partial stability on Hopfield neural networks with time delays,including attraction,stability and asymptotic stability,are obtained by using K-type functions and Lyapunov functions.Two discriminances about asymptotic stability of Bidirectional associative memory model,diagonal semi-stability conditions and semi-M matrix conditions,are obtained by constructing different Lyapunov functions.The asymptotic stability of Bidirectional associative memory models with time-varying delays are studied.The fact is confirmed that the Bidirectional associative memory models with time delays have the same stability as the BAM models without delays have if the time delays are bounded.The stability of Cellular neural networks with delay-type template and symmetrical parameters are investigated.It voids Hopfield neural networks methods and take advantage of Cellular neural networks templates.The equilibrium points are global asymptotic stable under the conditions presented and are dependent of input and bias current.Thus the equilibrium point needed can be designed in the application of optimization.By using some skillfully constructing Lyapunov function method and subtly estimating inequality method,a new result on global asymptotic stability of Cellular neural networks with time-varying delays is obtained.The conditions of the result given are concise and are morn convenient when applied than other corresponding conditions.Based on the importantly theoretic significance and applied value for dissipactivity studies on common neural networks,a dissipactivity result for Cellular neural networks with time-varying delays is given.A global attract set and positive invariability set of the model is included in the results.