New technique to quantify chaotic dynamics based on differences between semi-implicit integration schemes

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