Finite-time Passivity And Synchronization Of Coupled Complex-valued Memristor Neural Network

In nature and human society,complex networks are everywhere.Coupled neural network is also a type of complex network,which is composed of many mutually coupled neural networks.Coupled neural networks have received extensive attention due to their potential applications in all sorts of fields including image encryption,harmonic oscillation generation,system identification,etc.As a type of equivalent synaptic electronic component,memristor can bring good memory characteristic like brain.By replacing resistor with memristor in neural networks,memristive neural networks can better present neural processes in the human brain and have been successfully applied in various fields such as device modeling and signal processing.Although real-valued neural networks have produced many meaningful results in different fields,many problems in the real world cannot be solved in the real-valued fields.Compared with real-valued neural networks,complex-valued neural networks has more complex properties,not just simple extensions of real-valued one.Complex-valued neural networks can solve many problems that cannot be solved in the real domain,such as the XOR problem.In addition,Complex-valued neural networks are widely applied in practical aspects such as including image processing,antenna design,analogy amplification and so on.Therefore,the study of coupled complex-valued memristive neural networks is of practical and theoretical significance.In this paper,the finite-time passivity and synchronization issues of coupled complexvalued memristive neural networks are studied by virtue of deploying Lyapunov stability theory combined with some inequality techniques.First,coupled complex-valued memristive neural networks model is presented,finite-time passivity and synchronization conditions for coupled complex-valued memristive neural networks are derived by designing appropriate state feedback controller and Lyapunov functional as well as employing some new inequality techniques.Second,owing to the influence of delay on the network,we discuss the finite-time passivity and synchronization problems of the coupled complex-valued memristive neural networks with time-varying delay,and establish several finite-time passivity and synchronization criteria for corresponding network.Third,due to the model error combined with parameter interference,network model may generate parameter deviations.In consequence,the finite-time synchronization and robust finite-time synchronization issues of coupled complex-valued memristive neural networks are investigated,and several finite-time synchronization and robust finite-time synchronization criteria for considered are established.In addition,a lot of uncertain factors and disturbance is usually inevitable in the real world,which are possible to cause the networks into unexpected states and even break the synchronization.Thus,we also purse the study on the finite-time H∞ synchronization and robust finitetime H∞ synchronization problems for coupled complex-valued memristive neural networks.At last,we provide some numerical examples to illustrate the effectiveness of the obtained criteria.