基于广义忆阻器的Lü超混沌系统分析及其应用

Analysis and application of the Lu hyperchaotic system based on generalized memristor

引入一个双曲正切的广义压控忆阻器到Lü混沌系统中,增加混沌系统的复杂程度,构建了一个新型的四阶超混沌忆阻系统.采用Lyapunov指数、分岔图等非线性系统分析方法对忆阻系统进行理论分析,验证系统的超混沌特性.研究忆阻系统的动力学行为,对系统参数与初始值的改变进行分析,得到随参数变化引起的分岔与瞬态混沌现象和随初始值变化的吸引子共存现象.电路仿真及硬件电路验证了该忆阻超混沌系统的正确性与物理可实现性.将该忆阻超混沌系统应用于彩色图像加密中,具有良好的密钥敏感性和丰富的动力学特性,与加密算法结合后可用于保密通信领域.

A new fourth-order hyperchaotic memristor system was constructed by introducing a hyperbolic tangent generalized voltage-controlled memristor into the Li chaotic system to increase the complexity of the chaotic system.A theoretical analysis of this memristor system was carried out,and the nonlinear system analysis methods such as Lyapunov exponent and bifurcation diagram were used to verify the hyperchaotic properties of the system.The dynamic behavior of this memristor system was further investigated,and the bifurcation and transient chaotic phenomena caused by the change of parameters and initial values analyzed,and the attractor coexistence phenomena caused by the change of initial values obtained.Circuit simulations and hardware circuits were fabricated to verify the correctness and physical realizability of this memristive hyperchaotic system,which was then applied to color image encryption.The system has good key sensitivity and rich dynamics,and can be used in the field of secure communica-tion in combination with encryption algorithms.