Input-to-state Stability And Quasi-synchronization Of BAM Neural Networks

BAM neural networks(bidirectional associative memory neural networks),as a kind of artificial neural networks,are widely applied in pattern recognition and control.Generally speaking,BAM neural network systems are described by ordinary differential models,but Markovian systems or fractional order systems may be more accurate from the analysis of modeling accuracy.Based on the existing research results,this paper studies the input-to-state stability of BAM neural networks with Markovian jumps,the input-to-state stability of fractional BAM neural networks and quasi-synchronization of fractional BAM neural networks respectively.The first chapter introduces some basic theories about Markovian systems and fractional order systems and the current research status of BAM neural networks at home and abroad.In chapter 2,the input-to-state stability of BAM neural networks with time-varying delay and Markov jump parameters is discussed.Considering that the system has Markovian jump parameters,we choose an improved criterion,i.e.mean square exponential input-to-state stability.With the help of stochastic theory,we construct a Markov switching Lyapunov function,and obtain algebraic and linear matrix inequality(LMI)conditions for the mean square exponential input-to-state stability of the system by using weak infinitesimal operators.In addition,we design a controller to simplify algebraic conditions.Finally,we provide two numerical examples to illustrate the effectiveness and superiority of the obtained results.In chapter 3,the input-to-state stability of multi-delay fractional-order complex BAM neural networks is discussed.Different from the traditional integer-order differential equations with time delays,the stability of fractional-order systems with time delays is difficult to be determined by constructing integral terms in Lyapunov functional.Based on the properties of Mittag-Leffler functions,Laplace transform and inequality techniques,by designing the controller and constructing a non-negative function,a sufficient condition for the input-to-state stability of the system is derived.Finally,a simulation example is given to illustrate the effectiveness of the theoretical results.In chapter 4,the quasi-synchronization problem of delayed fractional quaternion BAM neural networks is studied.Here,instead of separating the systems into the real systems and the imaginary systems,we directly give the fractional inequality of the quaternion function,which generalizes the existing fractional complex inequality.By using this inequality and designing a linear feedback controller,the quasi-synchronization of fractional quaternion BAM neural networks can be realized.Finally,we give an example to verify the validity of our results.The fifth chapter summarizes the whole article,pointing out the innovation,deficiency and our future research directions.