Stability Analysis And Stabilization Control Of Neurodynamic Systems

As a special class of dynamic systems,neurodynamic system can mimic neuro-biological architectures to some extent.In the past decades,neurodynamic systems have received much attention for their immense applications in various areas such as biological,physical,economic and so forth.Such extensive applications are almost based on dynamical properties of neurodynamic systems in theory.Therefore,it is very interesting and important to study various aspects of neurodynamic systems.In this dissertation,several classes of neurodynamic systems are investigated.By employing the theory of differential equations with piecewise constant argument of generalized type,generalized Gronwall-inequality,fractional-order Leibniz rule and inequality techniques,some theoretical results are obtained.The main contents are draw up as follows:The global mean square exponential stability of stochastic neurodynamic system with retarded and advanced argument is investigated.Based on the theory of differential equations with piecewise constant argument of generalized type,several sufficient conditions depended on system parameters in forms of algebraic inequalities are established to ensure the existence and uniqueness of solution.Additionally,the relationship of system status in the current time and in the deviating function is revealed in detail.Besides,global mean square exponential stability is studied via the stability theory of stochastic differential equations.The Mittag-Leffler stability of a class of fractional-order neurodynamic systems in the presence of generalized piecewise constant arguments is studied.By applying theory of fractional-order differential equations,dynamic behavior of such system is analyzed clearly.The obtained results generalize the properties of integer-order systems,which also offer a new orientation to explore the characteristic of nonlinear control systems with piecewise constant arguments of generalized type.The global O(t-?)stabilization for a class of fractional-order memristive neurodynamic systems with time delays is discussed.Two kinds of control schemes are employed to stabilize such system via comparison principles of fractional-order systems.Several stabilization conditions in form of algebraic criteria are presented based on a new fractional-order Lyapunov function method and Leibniz rule.The derived criteria improve and extend the existing related results.The basic theories of dynamics on several classes of neurodynamic systems are probed.Such a study laid a foundation for developing the theories of nonliear systems.