Non-linear Circuit Analysis And Image Encryption Application Based On Memristor

The memristor,as a nonlinear element,is easy to generate chaotic oscillation signal in the circuits,which provides a new direction for the development of many engineering fields,such as electrical and electronics,artificial intelligence and nonlinear systems.Among them,the construction and application of the memristor-based chaotic circuits has been paid greatly attentions to researchers,and has become one of the hotspots in the field of nonlinearity.In this thesis,two kinds of memristive chaotic circuits are designed,and the complex nonlinear dynamic characteristics of two circuits are analyzed.Then,the proposed circuits are realized by digital circuit technology and analog circuit technology.Finally,the chaotic sequences generated by the memristive systems are used to complete the digitial image encryption.The main work is generalized as follows:(1)The nonlinear circuit with single absolute memristor is constructed,and the complex dynamic behavior of the system is analyzed.The memristor with absolute value is introducted into the improved Chua’s circuit,and then the new four-dimensional memristor circuit is constructed.It is found that the system exists special sysmmetric bifurcation and the multistability in the symmetric domains,which is different from Chua’s circuit and lays the foundation for the encryption of memristor chaotic sequences.At last,based on the analog electronic technology,the hardware experiment completed by the circuit discrete components are used to prove the correctness of the theoretical analysis and the physical realizability of the circuit.(2)The voltage-current model and the flux-charge model of the circuit with two different memristors are established,and the dynamical behaviors of two models are compared.The scheme of digitial circuit is designed to physically control multistability of the system.Firstly,based on the above memristor-based circuit,the memristor described by cubic nonlinear function is added,and the dual memristive circuit is designed.Then,according to Kirchhoff’s law and flux-charge analysis method,the two mathematical models are established and the dynamical behaviors are discussed by the conventional nonlinear dynamic analysis methods.It is helpful to define the domains of parameters or initial values corresponding to different motions.In addition,the feasibility and validity of flux-charge analysis method in heterogeneous dual memristive circuit are verified,which provides the theoretical reference for the analysis of similar nonlinear systems.Finally,through digital circuit implementation technology,the dual-memristor-based circuit is realized and the precise physical control of the multistability is completed.(3)Based on the masking encryption algorithm which combines the optimal scrambling algorithm with the diffusion algorithm,the digital image encryption system of memristive circuits are designed.First of all,the randomness of the chaotic sequences generated by the three models are tested,and the sequcences with good pseudo-random characteristic are chosen as the code of chaotic encryption.Subsequently,the nonrepeat scrambling algorithm of one-dimensional vector are got by optimizing conventional row and column scrambling algorithm.At the same time,a new diffusion algorithm is formed by adding the cyclic right shift operation into the modulo diffusion algorithm.Based on the proposed memristive models and the above algorithms,the new memeritor chaotic digital cryptosystem is designed.Ultimately,the security and reliability of three memristor-based cryptisystems are analyzed by the statistical characteristics of ciphertext and the sensitivity of key.