Abstract：In order to get more complex dynamical properties, a chaotic system with cubic polynomial taking absolute value function is designed. The theoretical model of the chaotic system is described by a set of nonlinear equations with three state variables. The basic properties and the dynamic characteristics of the system like phase diagram, time domain waveform, Lyapunov exponent, Poincaré map and bifurcation diagram are analyzed. Under certain parameter conditions, the system has periodic and chaotic properties, and there are coexistence attractors or aggregation attractors when the initial values are symmetrical. In addition, when some system parameters change, the system has constant dynamic characteristics, when the initial value of the state variable changes, the dynamic characteristics of the system also remain unchanged. The correctness of the theory is verified by circuit simulation. Based on the newly designed chaotic system, an encryption scheme is designed, and the encryption performance is analyzed, which shows the effectiveness of the encryption scheme.
高正中, 杜翔. 含多项式取绝对值函数的混沌系统分析与应用[J]. 复杂系统与复杂性科学, 2024, 21(1): 74-84.
GAO Zhengzhong, DU Xiang. Analysis and Application of Chaotic System with Polynomial Absolute Valued Function[J]. Complex Systems and Complexity Science, 2024, 21(1): 74-84.
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