Synchronization For Neural Networks With Delays Via Feedback Control

Synchronization is ubiquitous in real life and the synchronization of neural networks(NNs)is a widespread phenomenon in nature that cannot be ignored.Recently,the synchronization and control of NNs have attracted much attention from scholars.However,in the real NNs of physics,engineering,communication and other fields,the general decay synchronization(GDS),general decay lag synchronization(GDLS)and fixed-time synchronization and control of networks are more realistic and applied values although the related work is just beginning and the related results are very few.In view of this,some related theories,including ?-type function,Lipschtiz conditions,Lyapunov function,inequality techniques,are comprehensively used to investigate GDS and fixed-time synchronization of NNs with time-delays.The main content of this article can be summarized as follows:In the first part,the GDS of a class of bidirectional associative memory neural networks(BAMNNs)with time-varying delays is studied.First,a useful lemma which generalizes the classical exponential synchronization and polynomial synchronization is introduced.Then by using this lemma,some simple sufficient criteria ensuring the GDS of considered BAMNNs are obtained via designing a novel nonlinear feedback controller and using some inequality techniques.Finally,two numerical examples are provided to demonstrate the feasibility of the established theoretical results.In the second part,the GDLS problem for a class of competitive neural networks(CNNs)with constant delays via designing a novel nonlinear feedback controller is concerned.Based on the useful lemma,which guarantee the GDS of chaotic systems,some simple sufficient criteria ensuring the GDLS of addressed CNNs are obtained via constructing a novel Lyapunov function and using some inequality techniques.Finally,one numerical example is provide to demonstrate the feasibility of the established theoretical results.In the third part,the fixed-time synchronization of recurrent neural networks(RNNs)with discontinuous activations via discontinuous control strategy is investigated.Fixedtime synchronization means that synchronization can be achieved in a fixed time for any initial values of the considered systems.Based on constructing a novel Lyapunov function and analysis technique,some novel criteria are obtained to guarantee the fixedtime synchronization of considered networks via a control strategy.Finally,an example is provided to show the effectiveness and flexibility of the results derived in this paper.