Liu Shutong, Sun Zhongkui, Zhao Nannan
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China.
Chaos. 2020 Oct;30(10):103108. doi: 10.1063/5.0012212.
Introducing the fractional-order derivative into the coupled dynamical systems intrigues gradually the researchers from diverse fields. In this work, taking Stuart-Landau and Van der Pol oscillators as examples, we compare the difference between fractional-order and integer-order derivatives and further analyze their influences on oscillation quenching behaviors. Through tuning the coupling rate, as an asymmetric parameter to achieve the change from scalar coupling to non-scalar coupling, we observe that the onset of fractional-order not only enlarges the range of oscillation death, but attributes to the transition from fake amplitude death to oscillation death for coupled Stuart-Landau oscillators. We go on to show that for a coupled Van der Pol system only in the presence of a fractional-order derivative, oscillation quenching behaviors will occur. The results pave a way for revealing the control mechanism of oscillation quenching, which is critical for further understanding the function of fractional-order in a coupled nonlinear model.
将分数阶导数引入耦合动力系统逐渐引起了来自不同领域研究人员的兴趣。在这项工作中，以斯图尔特 - 兰道振子和范德波尔振子为例，我们比较了分数阶导数和整数阶导数之间的差异，并进一步分析它们对振荡猝灭行为的影响。通过调整耦合率，作为一个不对称参数以实现从标量耦合到非标量耦合的转变，我们观察到分数阶的出现不仅扩大了振荡死亡的范围，而且导致了耦合斯图尔特 - 兰道振子从虚假振幅死亡到振荡死亡的转变。我们接着表明，对于耦合范德波尔系统，只有在存在分数阶导数的情况下才会出现振荡猝灭行为。这些结果为揭示振荡猝灭的控制机制铺平了道路，这对于进一步理解分数阶在耦合非线性模型中的作用至关重要。
