分数阶忆阻Henon映射的可控多稳定性及其视频加密应用  

Controllable multistability of fractional-order memristive Henon map and its application in video encryption

作　　者：张红伟[1] 付常磊 潘志翔 丁大为[1] 王金 杨宗立[1] 刘涛 Zhang Hong-Wei;Fu Chang-Lei;Pan Zhi-Xiang;Ding Da-Wei;Wang Jin;Yang Zong-Li;Liu Tao(School of Electronics and Information Engineering,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学电子信息工程学院,合肥230601

出　　处：《物理学报》2024年第18期38-53,共16页Acta Physica Sinica

摘　　要：基于局部有源离散忆阻器构建一种能够产生任意数量共存吸引子的分数阶忆阻Henon映射.该映射的不动点数量由忆阻器内部参数控制,实现可控的同质多稳定性,适合基于混沌的工程应用.通过相图、分岔图、最大Lyapunov指数和吸引盆等方法揭示该映射的复杂动力学行为.数值模拟结果表明,该分数阶映射能够产生各种周期轨道、混沌吸引子和倍周期分岔等现象.随后使用ARM数字平台实现该系统,实验结果验证其物理可实现性.最后,基于该映射设计一种视频加密算法,并通过安全性分析验证该加密算法能够有效保证视频的安全传输.In recent years,the use of discrete memristors to enhance chaotic maps has received increasing attention.The introduction of memristors increases the complexity of chaotic maps,making them suitable for engineering applications based on chaotic systems.In this work,a fractional-order discrete memristor exhibiting local activity and controllable asymptotic stability points is constructed by using multiband nonlinear functions.The locally active property of this memristor is demonstrated by using the power-off plot and DC v-i plot.It is then introduced into the Henon map to construct a fractional-order memristive Henon map that can generate any number of coexisting attractors.Simulation results show that the number of fixed points in the system is controlled by the memristor parameters and related to the number of coexisting attractors,thus achieving controllable homogeneous multistability.The complex dynamical behaviors of this map are analyzed by using phase portraits,bifurcation diagrams,maximum Lyapunov exponent(MLE),and attractor basins.Numerical simulations show that the fractional-order map can generate various periodic orbits,chaotic attractors,and period-doubling bifurcations.The system is then implemented on an ARM digital platform.The experimental results are consistent with the simulation results,confirming the accuracy of the theoretical analysis and its physical feasibility.Finally,a parallel video encryption algorithm is designed by using the chaotic sequence iteratively generated by fraction-order memory Henon mapping,which mainly includes frame pixel scrambling and diffusion.Comprehensive security analyses are conducted,proving the robustness and reliability of the proposed encryption scheme.The results show that the encryption algorithm can effectively protect video information.In the future,we will explore other methods of constructing chaotic or hyperchaotic systems with controllable multistability and study their circuit implementation,synchronization control,and chaos-based engineering applicat

关 键 词：分数阶Henon映射 局部有源离散忆阻器 可控多稳定性 视频加密 

分 类 号：TN60[电子电信—电路与系统] O415.5[理学—理论物理]