Sun Zhongkui, Xiao Rui, Yang Xiaoli, Xu Wei
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China.
College of Mathematics and Information Science, Shaan'xi Normal University, Xi'an 710062, People's Republic of China.
Chaos. 2018 Mar;28(3):033109. doi: 10.1063/1.5019772.
Oscillation quenching has been widely studied during the past several decades in fields ranging from natural sciences to engineering, but investigations have so far been restricted to oscillators with an integer-order derivative. Here, we report the first study of amplitude death (AD) in fractional coupled Stuart-Landau oscillators with partial and/or complete conjugate couplings to explore oscillation quenching patterns and dynamics. It has been found that the fractional-order derivative impacts the AD state crucially. The area of the AD state increases along with the decrease of the fractional-order derivative. Furthermore, by introducing and adjusting a limiting feedback factor in coupling links, the AD state can be well tamed in fractional coupled oscillators. Hence, it provides one an effective approach to analyze and control the oscillating behaviors in fractional coupled oscillators.
在过去几十年里，振荡猝灭在从自然科学到工程学等诸多领域都得到了广泛研究，但迄今为止，相关研究仅限于具有整数阶导数的振荡器。在此，我们首次报道了分数阶耦合斯图尔特 - 兰道振荡器中部分和/或完全共轭耦合的振幅死亡（AD）研究，以探索振荡猝灭模式和动力学。研究发现，分数阶导数对AD状态有至关重要的影响。AD状态的区域随着分数阶导数的减小而增大。此外，通过在耦合链路中引入并调整一个极限反馈因子，分数阶耦合振荡器中的AD状态可以得到很好的控制。因此，它为分析和控制分数阶耦合振荡器中的振荡行为提供了一种有效的方法。
