非線形振動系におけるカオス的挙動の特徴について : 運動方程式が未知なる場合

概要

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To characterize chaotic oscillation arising in nonlinear systems, a method of statistical mechanics is applied. The chaotic oscillation is characterized in terms of the dynamic structure functions : the fluctuation spectrum, the q-weighted average and the q-weighted variance. In the previous paper, in order to obtain the local expansion rates that lead to the dynamic structure functions, the variational equations of motion were used. However the expansion rates cannot be obtained from the variational equations if the equations of motion are not known. Therefore, in the present paper, under the assumption that the equations of motion are not known, it is shown that the method of estimating matrices based on Poincare maps of ocsillation is applicable. As examples, the parametrically forced pendulum system and the Duffing system are taken up. The results of the method of estimating matrices are similar to those of the variational method.
1993-11-25