Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China.
Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China.
Chaos. 2022 Aug;32(8):083112. doi: 10.1063/5.0094685.
A moderate degree of diversity, in form of quenched noise or intrinsic heterogeneity, can significantly strengthen the collective response of coupled extended systems. As yet, related discoveries on diversity-induced resonance are mainly concentrated on symmetrically distributed heterogeneity, e.g., the Gaussian or uniform distributions with zero-mean. The necessary conditions that guarantee the arise of resonance phenomenon in heterogeneous oscillators remain largely unknown. In this work, we show that the standard deviation and the ratio of negative entities of a given distribution jointly modulate diversity-induced resonance and the concomitance of negative and positive entities is the prerequisite for this resonant behavior emerging in diverse symmetrical and asymmetrical distributions. Particularly, for a proper degree of diversity of a given distribution, the collective signal response behaves like a bell-shaped curve as the ratio of negative oscillator increases, which can be termed negative-oscillator-ratio induced resonance. Furthermore, we analytically reveal that the ratio of negative oscillators plays a gating role in the resonance phenomenon on the basis of a reduced equation. Finally, we examine the robustness of these results in globally coupled bistable elements with asymmetrical potential functions. Our results suggest that the phenomenon of diversity-induced resonance can arise in arbitrarily distributed heterogeneous bistable oscillators by regulating the ratio of negative entities appropriately.
一定程度的多样性，以淬火噪声或固有异质性的形式，可以显著增强耦合扩展系统的集体响应。然而，关于多样性诱导共振的相关发现主要集中在对称分布的异质性上，例如，具有零均值的高斯或均匀分布。保证异质振荡器中共振现象出现的必要条件在很大程度上仍然未知。在这项工作中，我们表明，给定分布的标准偏差和负实体的比例共同调节多样性诱导共振，并且负实体和正实体的共存是这种共振行为在各种对称和不对称分布中出现的前提条件。特别是，对于给定分布的适当多样性程度，随着负振荡器比例的增加，集体信号响应表现为钟形曲线，这可以称为负振荡器比诱导共振。此外，我们基于简化方程分析揭示了负振荡器比例在共振现象中的门控作用。最后，我们在具有不对称势函数的全局耦合双稳元件中检验了这些结果的稳健性。我们的结果表明，通过适当调节负实体的比例，多样性诱导共振现象可以在任意分布的异质双稳振荡器中出现。
