ある非線形振動系のカオス的挙動について　分数調波共振領域の応答特性

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  • Chaotic Behavior of a Nonlinear Vibrating System with a Retarded Argument (Characteristics in the Region of Subharmonic Resonance).
  • アル ヒセンケイ シンドウケイ ノ カオステキ キョドウ ニ ツイテ ブンスウ

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In this paper, we consider the characteristics of a nonlinear vibrating system, i. e., the van der Pol and Duffing equation, with a retarded argument under a harmonic exciting force. A numerical analytical procedure has been applied to analyze the characteristics in the subharmonic resonant region of the system. The system has been found to show quite complex charachteristics, e.g., many kinds of subharmonic oscillations, both symmetric and asymmetric subharmonic solutions, difurcations and nonperiodic solutions. Each of these subharmonics has shown isolated, island like response curves. With the use of numerical simulation, Poincare mapping, basin of attractions and chaotic phenomena, corresponding to nonperiodic solutions, have been obtained. The chaotic behavior appears in various frequency regions. These nonperiodic motions have been concluded to be chaotic because of the positive Lyapunov exponent. The route to chaos is via period doubling bifurcations.

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