Parametrically driven oscillators provide a natural platform for neuromorphic computation, where nonlinear mode coupling and intrinsic dynamics enable both memory and high-dimensional transformation. Here, we investigate a two-mode system exhibiting 2:1 parametric resonance and demonstrate its operation as a reservoir computer across distinct dynamical regimes, including sub-threshold, parametric resonance, and frequency-comb states. By encoding input signals into the drive amplitude and sampling the resulting temporal and spectral responses, we perform one step-ahead prediction of benchmark chaotic systems, including Mackey-Glass, Rossler, and Lorenz dynamics. We find that optimal computational performance is achieved within the parametric resonance regime, where nonlinear interactions are activated while temporal coherence is preserved. In contrast, although frequency-comb states introduce increased spectral dimensionality, their performance is not consistently good across their existence band and also degrades in the chaotic comb regime due to loss of phase coherence. Mapping prediction error over parameter space reveals a direct correspondence between computational capability and the underlying bifurcation structure, with low-error regions aligned with the parametric resonance boundary. We further show that the input modulation, the detuning from the frequency matching condition, damping ratio, and input data rate systematically control the accessible dynamical regimes and thereby the computational performance. These results establish parametric resonance as a robust operating regime for oscillator-based reservoir computing and provide design principles for tuning physical systems toward optimal neuromorphic functionality.

翻译：参量驱动振荡器为神经形态计算提供了天然平台，其非线性模式耦合与内在动力学特性可同时实现记忆存储与高维变换。本文研究呈现2:1参量共振的双模系统，并展示其在亚阈值、参量共振与频率梳态等不同动力学区域中作为储备池计算机的运行机制。通过将输入信号编码为驱动振幅并采集时域与频域响应，我们对Mackey-Glass、Rössler和Lorenz等基准混沌系统执行单步预测。研究发现，最优计算性能出现在参量共振区域——该区域在保持时间相干性的同时激活非线性交互。相比之下，尽管频率梳态引入更高的频谱维度，但其性能在其存在频带内并非始终稳定，且因相位相干性丧失而在混沌梳态区域中性能退化。通过绘制参数空间内的预测误差图，发现计算能力与底层分岔结构存在直接对应关系，低误差区域与参量共振边界高度吻合。进一步研究表明，输入调制、频率匹配条件的失谐量、阻尼比及输入数据速率可系统控制可达动力学区域，进而调控计算性能。这些结果确立了参量共振作为振荡器型储备池计算的稳健工作模式，为优化物理系统实现神经形态功能提供了设计准则。