Comparing the algorithms of multiparametric bifurcation analysis

In this paper we present the comparative study of different bifurcation analysis techniques for nonlinear dynamical systems research. The study is given through a comparison of algorithms for multiparametric diagram plotting. Thomas chaotic attractor is considered as a test dynamical system. The paper reviews statistical histogram algorithm, the kernel density estimation (KDE) algorithm and classical approach of Lyapunov exponent calculation. It is shown that KDE algorithm is superior for plotting bifurcation diagrams on short simulation times. The quantitative estimation of the effectiveness of various nonlinear system investigation algorithms and detailed data about Thomas chaotic system behavior are given.