Design Of Memristive Cellular Neural Network Chaotic System And Its Application In Image Encryption

Cellular neural networks combine the advantages of traditional artificial neural networks and cellular automata and are widely used in the construction and research of intelligent systems.In recent years,with the preparation and research of the fourth basic circuit element-memristor,the memrisive cellular neural network has become the focus and hot topic of many scholars’ research,which is constructed by combining memristors with cellular neural network.In order to study the chaotic phenomena that may occur in the microscopic axons,single cells,and coupled cells in the brain nervous system,designing a suitable memristive chaotic cellular neural network model is an important research content of nonlinear systems.Therefore,combined with the latest research results of the memristive artificial neural network chaotic system,this paper constructs several types of memristive cellular neural network chaotic systems with complex dynamic behavior,analyzes the dynamic behavior of such systems,designs the analog circuit,and finally,applies these systems to image encryption.The main work and contributions of this paper include the following three aspects:1.A cellular neural network chaotic system based on a flux-controlled memristor is constructed,and the influence of electromagnetic induction on the chaotic dynamical behavior of the system is analyzed.By adjusting the parameters related to the change of magnetic flux of the memristor to simulate the electromagnetic field change caused by electromagnetic radiation in the actual scene,the experimental results show that the system presents rich dynamic phenomena such as multi-period,forward and reverse period bifurcation,coexistence attractor,continuous chaos,transient chaos,and bistability.Then,an image encryption algorithm based on this system is proposed,and the effectiveness of the algorithm is proved by analyzing the information entropy,correlation,robustness,and time complexity of the algorithm.2.A memristor cell neural network chaotic system capable of generating a third type of multi-vortex chaotic attractor was constructed,and applied to the image encryption algorithm.Firstly,a mathematical model of memristor with the memristor function as even function and the internal state function as a hyperbolic tangent piecewise linear function is constructed,and the weight of the cellular neural network is realized by using this memristor to design a new cell neural network chaotic system.By analyzing the equilibrium point of the system and its eigenvalue characteristics,it is found that there are unstable saddle focus equilibrium points of index 1 and index 2 in the system,in particular,when adjusting the piecewise linearity of the internal state function of the memristor,the number of unstable saddle focus equilibrium points of index 2 of the system does not increase accordingly,but moves along the axial ends of the magnetic flux variable(φ).In addition,it is found that the system has dynamic behaviors such as initial value bias coexistence and amplitude control.Finally,a new image encryption algorithm is proposed and its performance is analyzed.3.A memristor cell neural network chaotic system capable of generating the first type of multi-scroll chaotic attractor was constructed,and the effectiveness of the system was verified by designing the system simulation circuit.Firstly,a single weight of the three-dimensional cellular neural network is realized by a memristor with the internal state function as a piecewise linear symbolic function,and the output function of the cellular neural network is a hyperbolic tangent function,which can more accurately simulate the changing characteristics in the biological neural network.Then,the equilibrium point and stability of the system are studied,and the mechanism behind the controllable behavior of the system to produce multi-scroll is clarified.Then,the phase trajectory diagram,bifurcation plot and Lyapunov index spectrum of the system are studied,and it is found that there is amplitude control and extreme multi-stable behavior in the system.In order to verify the feasibility of the system,the hardware circuit of the system is implemented with common discrete components.Finally,apply this system to image encryption.At the end of the paper,the research content of the whole text is summarized,and the future research work is prospected,and it is expected that some good results will be achieved in the future in the physical modeling of memristors and the implementation of neural network chaotic systems.