Dynamics In Inertial Cohen-Grossberg Neural Networks And Quaternion-Valued Neural Networks

In the last decades,neural networks have received widespread interests from researchers due to their wide applications in various fields such as pattern recognition,associative memory,parallel computing and image processing.Among them,the Cohen-Grossberg neural network(CGNN)is the most representative one since it comprises many popular neural networks as its special cases,such as Hopfield neural networks and cellular neural networks.It is rather general and can describe a number of models arising from neurobiology,population biology and evolution theory.Meanwhile,the introduction of the inertia item can be regarded as a powerful tool to generate complicated bifurcation behavior and chaos in a networked system.On the other hand,the dynamics of quaternion-valued neural networks have been an active research topic in recent years.Due to the simple representation of quaternion and the high efficiency in dealing with the multidimensional data,the quaternion-valued neural networks have been applied in an expansive field of applications and demonstrated better performances than the complex-valued neural networks and the real-valued neural networks.Therefore,the dynamics of inertial Cohen-Grossberg neural networks and quaternion neural networks are investigated in this doctoral thesis.The main innovations of this thesis can be summarized as follows.1.The global asymptotical stability of inertial Cohen-Grossberg neural networks with Markovian jumping parameters is studied.Firstly,by employing variable transformation,the considered system is equivalently divided into two first-order differential equations.Combining the Lyapunov stability theory,differential mean value theorem,delay segmentation method and linear matrix inequality techniques,we obtain some novel sufficient conditions to guarantee the global asymptotical stability of the addressed system.2.This thesis investigates the issue on adaptive synchronization of delayed inertial CohenGrossberg neural networks.By adopting the method of variable transformation,the addressed model,which includes the so-called inertial term,is transformed into two first-order differential equations.On the basis of the Lyapunov stability theory and the Lasalle invariant principle of functional differential equations,a novel and analytic scheme which ensures the adaptive synchronization between the drive-response system is proposed in component form,which can be readily verified.It is worth mentioning that we only need to impose one controller to the spilt systems to realize the adaptive synchronization,which is of less conservatism.3.The stability analysis of quaternion-valued neural networks with both leakage delay and additive time-varying delays is proposed.Without any decomposition,the reciprocally convex inequality is extended to the quaternion domain based on the quaternion matrix theory.By employing the Lyapunov-Krasovskii functional method and several inequality techniques,and fully considering the relationship between time-varying delays and upper bounds of delays,some sufficient criteria are derived to ensure the global asymptotical stability of the addressed system.4.The state estimation problem for delayed quaternion-valued neural networks of neutral type is addressed.Based on the Lyapunov stability theory and the quaternion matrix theory,several sufficient conditions are derived by adopting the free weighting matrix method and some matrix inequality techniques such that the addressed error-state system is globally asymptotically stable.The obtained criterion can be solved directly via the YALMIP toolbox in Matlab.5.This thesis is also dedicated to investigating the robust state estimation problem for the delayed uncertain quaternion-valued neural networks.We design an appropriate state estimator for the uncertain quaternion-valued neural networks via the available output measurements.Combing the Lyapunov functional method and several matrix inequality techniques,some delay-dependent conditions are presented for the existence of the desired state estimator.