A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes. Further, we examine the intriguing possibility of obtaining reliable logic outputs from a noise-free bistable system, subject only to periodic forcing, and show that this system also yields a phenomenon analogous to LSR, termed Logical Vibrational Resonance (LVR), in an appropriate window of frequency and amplitude of the periodic forcing. Lastly, this approach is extended to realize morphable logic gates through the Logical Coherence Resonance (LCR) in excitable systems under the influence of noise. The results are verified with suitable circuit experiments, demonstrating the robustness of the LSR, LVR and LCR phenomena. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

中文翻译：

---

利用非线性系统中的共振现象构建逻辑门

已发现由两个输入驱动的双态系统在中等噪声的最佳窗口中一致地产生反映两个输入的逻辑函数的响应。这种现象称为逻辑随机共振 (LSR)。我们扩展了传统的 LSR 范式，通过精心设计的耦合方案来实现更高级别的逻辑架构或典型的数字电子结构。此外，我们研究了从无噪声双稳态系统获得可靠逻辑输出的有趣可能性，仅受周期性强迫，并表明该系统也产生类似于 LSR 的现象，称为逻辑振动共振 (LVR)，在适当的周期强迫的频率和幅度窗口。最后，这种方法被扩展到通过在噪声影响下的可激发系统中的逻辑相干共振 (LCR) 来实现可变形逻辑门。结果通过合适的电路实验得到验证，证明了 LSR、LVR 和 LCR 现象的鲁棒性。本文是主题问题“驱动非线性系统中的振动和随机共振（第 1 部分）”的一部分。