Many novel chaotic systems have recently been identified and numerically studied. Parametric chaotic sets are a valuable tool for determining and classifying oscillation regimes observed in nonlinear systems. Thus, efficient algorithms for the construction of parametric chaotic sets are of interest. This paper discusses the performance of algorithms used for plotting parametric chaotic sets, considering the chaotic Rossler, Newton-Leipnik and Marioka-Shimizu systems as examples. In this study, we compared four different approaches: calculation of largest Lyapunov exponents, statistical analysis of bifurcation diagrams, recurrence plots estimation and introduced the new analysis method based on differences between a couple of numerical models obtained by semi-implicit methods. The proposed technique allows one to distinguish the chaotic and periodic motion in nonlinear systems and does not require any additional procedures such as solutions normalization or the choice of initial divergence value which is certainly its advantage. We evaluated the performance of the algorithms with the two-stage approach. At the first stage, the required simulation time was estimated using the perceptual hash calculation. At the second stage, we examined the performance of the algorithms for plotting parametric chaotic sets with various resolutions. We explicitly demonstrated that the proposed algorithm has the best performance among all considered methods. Its implementation in the simulation and analysis software can speed up the calculations when obtaining high-resolution multi-parametric chaotic sets for complex nonlinear systems.

最近已经发现了许多新颖的混沌系统并进行了数值研究。参数混沌集是确定和分类在非线性系统中观察到的振动状态的有价值的工具。因此，感兴趣的是用于构造参数混沌集的有效算法。本文以混沌Rossler，Newton-Leipnik和Marioka-Shimizu系统为例，讨论了用于绘制参数混沌集的算法的性能。在这项研究中，我们比较了四种不同的方法：最大Lyapunov指数的计算，分叉图的统计分析，递归图估计，并基于基于半隐式方法获得的两个数值模型之间的差异引入了新的分析方法。所提出的技术允许人们区分非线性系统中的混沌运动和周期性运动，并且不需要任何其他程序，例如解归一化或初始散度值的选择，这无疑是其优势。我们使用两步法评估了算法的性能。在第一阶段，使用感知哈希计算来估算所需的仿真时间。在第二阶段，我们检查了绘制具有各种分辨率的参数混沌集的算法的性能。我们明确证明了所提出的算法在所有考虑的方法中均具有最佳性能。在复杂的非线性系统中获得高分辨率的多参数混沌集时，其在仿真和分析软件中的实现可以加快计算速度。