In this paper,we first propose a memristive chaotic system and implement it by circuit simulation.The chaotic dynamics and various attractors are analysed by using phase portrait,bifurcation diagram,and Lyapunov exponents.In particular,the system has robust chaos in a wide parameter range and the initial value space,which is favourable to the security communication application.Consequently,we further explore its application in image encryption and present a new scheme.Before image processing,the external key is protected by the Grain-128a algorithm and the initial values of the memristive system are updated with the plain image.We not only perform random pixel extraction and masking with the chaotic cipher,but also use them as control parameters for Brownian motion to obtain the permutation matrix.In addition,multiplication on the finite field GF(2^(8))is added to further enhance the cryptography.Finally,the simulation results verify that the proposed image encryption scheme has better performance and higher security,which can effectively resist various attacks.
A five-value memristor model is proposed,it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current.Then,based on the classical Liu-Chen system,a new memristor-based fourdimensional(4D)chaotic system is designed by using the five-value memristor.The trajectory phase diagram,Poincare mapping,bifurcation diagram,and Lyapunov exponent spectrum are drawn by numerical simulation.It is found that,in addition to the general chaos characteristics,the system has some special phenomena,such as hidden homogenous multistabilities,hidden heterogeneous multistabilities,and hidden super-multistabilities.Finally,according to the dimensionless equation of the system,the circuit model of the system is built and simulated.The results are consistent with the numerical simulation results,which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.
