Lei Xiaoqi, Liu Weiqing, Zou Wei, Kurths Jürgen
School of Science, Jiangxi University of Science and Technology, Ganzhou341000, China.
School of Mathematical Sciences, South China Normal University, Guangzhou510631, People's Republic of China.
Chaos. 2019 Jul;29(7):073110. doi: 10.1063/1.5093919.
Effects of a low-pass active filter (LPAF) on the transition processes from oscillation quenching to asymmetrical oscillation are explored for diffusively coupled oscillators. The low-pass filter part and the active part of LPAF exhibit different effects on the dynamics of these coupled oscillators. With the amplifying active part only, LPAF keeps the coupled oscillators staying in a nontrivial amplitude death (NTAD) and oscillation state. However, the additional filter is beneficial to induce a transition from a symmetrical oscillation death to an asymmetrical oscillation death and then to an asymmetrical oscillation state which is oscillating with different amplitudes for two oscillators. Asymmetrical oscillation state is coexisting with a synchronous oscillation state for properly presented parameters. With the attenuating active part only, LPAF keeps the coupled oscillators in rich oscillation quenching states such as amplitude death (AD), symmetrical oscillation death (OD), and NTAD. The additional filter tends to enlarge the AD domains but to shrink the symmetrical OD domains by increasing the areas of the coexistence of the oscillation state and the symmetrical OD state. The stronger filter effects enlarge the basin of the symmetrical OD state which is coexisting with the synchronous oscillation state. Moreover, the effects of the filter are general in globally coupled oscillators. Our results are important for understanding and controlling the multistability of coupled systems.
针对扩散耦合振子，研究了低通有源滤波器（LPAF）对从振荡猝灭到非对称振荡的过渡过程的影响。LPAF的低通滤波器部分和有源部分对这些耦合振子的动力学表现出不同的影响。仅使用放大有源部分时，LPAF可使耦合振子保持在非平凡振幅死亡（NTAD）和振荡状态。然而，额外的滤波器有利于诱导从对称振荡死亡到非对称振荡死亡，再到两个振子以不同振幅振荡的非对称振荡状态的转变。对于适当给出的参数，非对称振荡状态与同步振荡状态共存。仅使用衰减有源部分时，LPAF可使耦合振子处于丰富的振荡猝灭状态，如振幅死亡（AD）、对称振荡死亡（OD）和NTAD。额外的滤波器倾向于通过增加振荡状态与对称OD状态共存的区域来扩大AD区域，但缩小对称OD区域。更强的滤波效果会扩大与同步振荡状态共存的对称OD状态的吸引域。此外，滤波器的影响在全局耦合振子中是普遍存在的。我们的结果对于理解和控制耦合系统的多稳定性具有重要意义。
