关键词: Julia分形, 双涡卷混沌系统, 双参数, 电路仿真, 单片机

Abstract: In order to obtain a complex scroll chaotic system, a new system was constructed by applying the Julia fractal with a scroll structure to the deformed Liu system. The main characteristics such as phase diagram, equilibrium point, Lyapunov exponent spectrum and bifurcation diagram were analyzed. The power and fractional unit circuits of the system were designed on the Multisim platform, and the digital circuit of the new system was implemented using a microcontroller. The results show that the new system produces a more diverse form of four-winged double-scroll attractor, and the introduction of the coefficient k of the quadratic term does not change the shape of the attractor, only affecting the size of the attractor. Corresponding to the same parameter a, changing the coefficient k, the value of the maximum Lyapunov exponent remains unchanged, the coefficient k does not affect chaotic state of the system. Adopting modular circuit design can make the circuit more clear and the parameter adjustment more convenient. The results of the circuit simulation and the digital circuit implementation are consistent with the numerical calculation results performed in MATLAB, thus validating the feasibility of the combination of fractal and chaos.

Key words: Julia fractal, double-scroll chaotic system, two-parameter, circuit simulation, microcontroller