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.

中文翻译：

---

具有不同分布异质性的全局耦合双稳态系统中的多样性引起的共振

适度的多样性，以抑制噪声或内在异质性的形式，可以显着增强耦合扩展系统的集体响应。迄今为止，关于多样性引起的共振的相关发现主要集中在对称分布的异质性上，例如高斯分布或零均值均匀分布。保证异质振荡器中出现共振现象的必要条件仍然很大程度上未知。在这项工作中，我们表明，给定分布的标准差和负实体的比率共同调制多样性引起的共振，并且负实体和正实体的共存是在不同的对称和不对称分布中出现这种共振行为的先决条件。特别是，对于给定分布的适当程度的多样性，随着负振荡器比率的增加，集体信号响应表现得像钟形曲线，这可以称为负振荡器比率引起的谐振。此外，我们在简化方程的基础上分析揭示了负振荡器的比率在共振现象中起着门控作用。最后，我们检查了具有不对称势函数的全局耦合双稳态元件中这些结果的稳健性。我们的结果表明，通过适当调节负实体的比例，可以在任意分布的异质双稳态振荡器中出现多样性引起的共振现象。