Research On Synchronization Control And Applications Of Memristive Neural Networks With Time-Varying Delays

As we know,artificial neural network is derived from biological neural network system.The research purpose of artificial neural network is to gradually realize the highly intelligent neural network system by continuously simulating the structure and the mechanism of human brain neural network.With the memory capabilities,low power consumption,and easy integration,memristors are considered as the best electronic device for simulating the synapses of biological neurons.Memristors are adopted to simulate neuronal synapses instead of resistors,and the neural network is called memristive neural networks.At the same time,neural network is also a highly nonlinear network structure,which has the characteristics of dynamic behavior of nonlinear systems,and synchronization is also very important for the memristive neural networks.Combined with appropriate control technology,memristive neural networks can achieve many kinds of system synchronization.Memristive neural networks and the synchronization have important applications in signal transmission,pattern recognition and other fields.Regardless of artificial neural networks or biological neural networks,delays usually exist while the signals transmit between the neurons,which cause the system to oscillate and disrupt the stability of the system.Therefore,it is necessary to consider the problem of time delays in the neural network system.In addition,the memristor also has a special hysteresis loop characteristic,so that memristive neural network may appear more dynamic behaviors,showing some characteristics of chaotic systems.With these chaotic dynamic behaviors,memristive neural network and its synchronization control theory can also be applied to secure communication,information storage,image encryption,and pseudo-random number generation.This paper mainly studies the finite-time projective synchronization of memristive neural networks with time-varying delays,and the finite-time modified projective synchronization,finite-time lag synchronization,fixed time synchronization of memristive neural networks with multi-links and time-varying delays.The application of memristive neural networks with multi-links and time-varying delays,and the application of these synchronization theories.The main contributions of this paper are listed as follows:1.For memristive neural networks with leakage delay,time-varying discrete delay,and time-varying distributed delay,we study the finite-time projective synchronization control,and include two aspects of this work:in the first part,by designing a delay-independent controller and using a novel finite-time synchronization analysis method,we study the finite-time modified projective synchronization problem of memristive neural networks with time-varying delays.The controller here is very simple.At the same time,a secure communication scheme is proposed with this synchronization theory.In the second part,by designing delay-dependent feedback controller,combined with another finite-time synchronization theory,we propose the finite-time modified function projective synchronization criterion for memristive neural networks with time-varying delays,which is suitable for arbitrary bounded and differentiable projective functions.The relationship of modified projective synchronization,projective synchronization,anti-synchronization,modified function projective synchronization and function projective synchronization are discussed in the corollaries.2.Since the connections between neuron synapses are multi-connected,memristive neural networks with multi-links can reflect this feature better,leakage delay and discrete time-varying delays are introduced.Aiming at this model of multilateral memristive time-delay neural network,two finite time modified projective synchronization criteria are proposed,Based on this memristive neural networks with multi-links and delays,finite-time modified projective synchronization criteria are proposed.By designing the delay-dependent feedback controller and an adaptive controller,different finite-time synchronization analysis methods are used to implement the finite-time modified projective synchronization of memristive neural networks with multi-links and time-varying delays,respectively.In the analysis process of the theorems,the theories of differential inclusion and set-valued mapping are used to solve the memristive jump problem,and the synchronization problem is transformed into the stability problem of the error system under Filippov's discontinuity theory on the right.We give the preconditions for the boundedness of the activation function and the external input,which effectively solves the problem brought by the activation function and external input function in the proof.In addition,an image transmission scheme is designed with the modified projective synchronization.Simulation experiments verify the validity of the conclusions obtained.3.We study the finite-time lag synchronization of memristive neural networks with multi-links and time-varying delays,and the model considers discrete and distributed time-varying delays.The main work of this research is that,the adaptive control technology is used to design two controllers,which are delay-dependent and delay-independent,and we combine different finite-time synchronization control methods to achieve finite-time lag synchronization of memristive neural networks with multi-links and time-varying delays.In this study,three important lemmas are given by using the linear matrix inequality method,which solve the problem of parameter mismatch and simplify the process of proving the theorem.With the lag synchronization theorem and the idea of signal mixed modulation,a secure communication scheme is proposed.The experiments verify the validity of the theory and the feasibility of the scheme.4.This research is focused on the fixed time synchronization control and related applications of memristive neural networks with multi-links and time-varying delays,which includes three parts.In the first part,a quantitative feedback controller is designed by using a logarithmic method,combined with two fixed time synchronization theories,we study the fixed time synchronization control of memristive neural networks with multi-links and time-varying delays,and two calculation methods of fixed times are obtained.The quantitative interval replacement method and linear matrix inequality are used to solve the jump problem caused by the quantizer in the theoretical proof process.In the second part,based on the fixed time synchronization of memristive neural networks with multi-links and time-varying delays,with the signal masking method and adaptive signal systems,a secure communication scheme is proposed and verified by simulation experiments.The third part is the research on the application of memristive neural networks with multi-links and time-varying delays in image encryption.Based on the dynamic behaviors of memristive neural networks with multi-links and time-varying delays,a cryptographic sequence generator is designed,with the method of chaotic scrambling,an image encryption and decryption scheme is proposed and the experiments verify the feasibility.A key sequence generation algorithm is also proposed here to increase the key space.Apparently,many security analysis methods,includes histogram,key space,information entropy,peak signal-to-noise ratio,and correlation of neighboring pixels,are adapted to prove that the proposed scheme not only achieves a good image encryption effect,but also can effectively resist exhaustive attacks and statistical attacks.