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An oscillation in a dynamical system can be easily localized numerically if initial conditions from its open neighborhood lead to long-run behavior that approaches the oscillation. Such an oscillation (or set of oscillations) is called an attractor, and its attracting set is called the basin of attraction. Thus, from a computational point of view the following classification of attractors based on the simplicity of finding basin of attraction in the phase space is suggested:〔 〕〔 〕 an attractor is called a hidden attractor if its basin of attraction does not intersect with small neighborhoods of equilibria, otherwise it is called a self-excited attractor. ==Self-excited attractor localization== Self-excited attractors can be localized numerically by the standard computational procedure, in which after a transient process a trajectory, started from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation therefore one can easily identify it. Here It is essential to consider numerical localization procedures in forward and backward time, since computation in backward time may localize also an unstable oscillation. Classical attractors in the well-known dynamical systems of Van der Pol, Beluosov–Zhabotinsky, Lorenz, Rössler, Chua and many others are self-excited attractors and can be obtained numerically, with relative ease, by standard computational procedures described above. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hidden oscillation」の詳細全文を読む スポンサード リンク
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