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Stable limit cycle (shown in bold) for the [[Van der Pol oscillator]]

Stable limit cycle (shown in bold) for the [[Van der Pol oscillator]]

[[范德波尔振荡器]]的稳定极限环(粗体显示)

'''<font color="#ff8000">范德波尔振荡器 Van der Pol oscillator</font>'''的稳定极限环(粗体显示)

In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some nonlinear systems. Limit cycles have been used to model the behavior of a great many real-world oscillatory systems.  The study of limit cycles was initiated by Henri Poincaré (1854–1912).

In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some nonlinear systems. Limit cycles have been used to model the behavior of a great many real-world oscillatory systems.  The study of limit cycles was initiated by Henri Poincaré (1854–1912).

在数学上，在二维相空间动力系统的研究中，极限环是一个在相空间中的闭合轨迹，它具有当时间趋于无穷大或时间趋于负无穷大时至少有一条其他轨迹螺旋进入的性质。这种行为在一些非线性系统中表现出来。极限环已经被用来模拟许多实际振动系统的行为。对极限环的研究是由 Henri poincaré (1854-1912)提出的。

在'''<font color="#ff8000">数学 Mathematics</font>'''上，在二维'''<font color="#ff8000">相空间 Phase Space</font>''''''<font color="#ff8000">动力系统 Dynamical Systems</font>'''的研究中，'''极限环'''是一个在相空间中的闭合'''<font color="#ff8000">轨迹 Trajectory</font>'''，它具有当时间趋于无穷大或时间趋于负无穷大时至少有一条其他轨迹螺旋进入的性质。这种行为在一些'''<font color="#ff8000">非线性系统 Nonlinear Systems</font>'''中表现出来。极限环已经被用来模拟许多实际振动系统的行为。对极限环的研究是由 Henri poincaré (1854-1912)提出的。