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[en] Highlights: → The chaotic dynamical behavior first has been controlled by random phase. → It can be proved that chaos has been suppressed from the Lyapunov exponents. → It is verified that chaos has been suppressed from Poincare map. - Abstract: As the analysis of the chaotic dynamical behavior of a parametric Duffing's system, we show that chaos can be suppressed by addition the Gauss white noise phase and determined by the sign of the top Lyapunov exponent, which is based on the Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. Also Poincare map analysis is carried out to confirm the obtained results. So random phase can be realized as one of the methods of chaos control.
[en] Uniform index is a conception that can describe the uniformity of a finite point set in a polyhedron, and is closely related to chaos. In order to study uniform index, the concept of contained uniform index is defined, which is similar to uniform index and has good mathematical properties. In this paper, we prove the convergence of the contained uniform index, and develop the base of proving the convergence of uniform index.