Research Of Synchronization In Finite Time For Several Classes Of Neural Networks

The nonlinear systems described by fractional calculus have received extensive attention from researchers due to their memory characteristics.In particular,the dynamics of fractional-order neural networks as a special class of fractional-order systems has become one of the research hot pots in mathematics and information science.This thesis studies the global finite time synchronization problem of neural network systems.The main work is as follows:Firstly,under the assumption that the fractional order is time-varying and satisfies 0 <?(t)< 1,using the Lyapunov functional method,the Mittag-Leffler function and the linear matrix inequality analysis technique under the designed controller.The global finite time synchronization condition of time-varying fractional discontinuous neural network system is obtained.An accurate estimate of the upper bound of the synchronous dwell time is givenSecondly,by designing a state feedback controller with time delay and discontinuity,the Lyapunov functional method and non-smooth analysis technique are applied to propose the global finite time synchronization condition of the discontinuous delay neural network.The upper bound estimation expression of synchronous dwell time is given.Finally,by designing appropriate feedback controllers and using Lyapunov functional method and matrix inequality analysis technique,the global Mittag-Leffler anti-synchronization condition of linear matrix inequalities in fractional-order delay neural networks is established.the correctness of all the theoretical results established above and the feasibility of the design method are verified by numerical examples.