In this paper,phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied.The dynamics of such a system are obtained using the describing function method,and the necessary conditions for phase synchronization are also achieved.Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods.The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher,between,or lower than the highest,in between,or lowest natural frequency of the aggregate oscillators.Several numerical examples simulate the different cases versus the various synchronization frequency delays.
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机译:本文研究了两个具有延迟耦合的同步Van der Pol振荡器的相位同步和频率,使用描述函数方法获得了该系统的动力学特性,并获得了实现相位同步的必要条件。相较于其他传统方法,同步频率的最大优势是描述函数方法的主要优势。基于此方法获得的方程式证明了耦合振荡器在高于或低于最高频率之间或高于最高频率之间的频率同步现象。 ,或者说是总振荡器的最低固有频率。几个数值示例可以模拟不同情况以及各种同步频率延迟。
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