荷控型忆阻混沌系统的动力学及图像加密应用  

Dynamic Analysis and Image Encryption Application of Charge controlled Memristor Chaotic Systems

作　　者：吕小红[1] 程百信 周文君 LYU Xiaohong;CHENG Baixin;ZHOU Wenjun(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《兰州交通大学学报》2025年第1期39-48,共10页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(12062008)。

摘　　要：设计了一个四维荷控型忆阻混沌电路,建立了相应状态变量的动力学方程。分析了平衡点的稳定性,结合分岔图、Lyapunov指数谱和相轨图等研究了初始条件对系统运行状态的影响,以及系统在一定电路参数和初值条件下的瞬态行为。运用分块理论和DNA编码的加密算法对图像进行了直方图、相邻像素相关性、密匙敏感性和信息熵分析。结果表明:改变忆阻器内部状态变量的初值可以产生五种不同类型的吸引子,反映了系统动力学对初始条件的敏感性;在不同的电路参数和初值条件下,系统具有瞬态混沌、间歇性混沌和状态转移等复杂的非线性动力学行为;基于荷控型忆阻混沌系统的加密算法安全性较高,统计性能分析反映了图像加密算法的有效性,展示了该算法在安全通信中的潜在应用。A four order charge controlled memristor chaotic circuit is designed,and the dynamic equation of corresponding state variables is established.The stability of the equilibrium point is analyzed.The influence of initial conditions on the operating stateas well as the transient behavior under certain circuit parameters and initial conditions of the system is studied by combining bifurcation diagrams,Lyapunov exponent spectra,and phase trajectory diagrams.The block theory and DNA coding are applied to analyze the histogram,adjacent pixel correlation,key sensitivity,and information entropy of the image.The results indicate that changing the initial value of the internal state variables of the memristor can generate five different types of attractors,reflecting that the sensitivity of system dynamics to initial conditions;Under different circuit parameters and initial conditions,the system exhibits complex nonlinear dynamical behaviors such as transient chaos,intermittent chaos,and state transitions;The encryption algorithm based on the charge controlled memristive chaotic system has high security,and the statistical performance analysis reflects the effectiveness of the image encryption algorithm,and shows the potential application of the algorithm in secure communication.

关 键 词：混沌系统 忆阻器 瞬态行为 图像加密 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]