We consider a model reaction-diffusion system with two coupled layers in which one of the components in a layer is parametrically driven by a periodic force. On perturbation of a homogeneous stable steady state, the system exhibits parametric instability inducing synchronization in temporal oscillation at half the forcing frequency in absence of diffusion and spatiotemporal patterns in presence of diffusion, when strength of parametric forcing and the strength of coupling are kept above their critical thresholds. We have formulated a general scheme to derive analytically the critical thresholds and dispersion relation to locate the unstable spatial modes lying between the tilted Arnold tongue in the amplitude-frequency plot. Full numerical simulations on Gierer-Meinhardt activator-inhibitor model corroborate our theoretical analysis on parametric instability-induced antiphase synchronization in chemical oscillation and spatiotemporal pattern formation, between the two layers.

中文翻译：

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化学振荡和时空模式中的参数不稳定性诱导同步

我们考虑具有两个耦合层的模型反应扩散系统，其中层中的一个组件由周期力参数化驱动。在均质稳定稳态的扰动下，当参数强迫的强度和耦合强度保持在其之上时，系统表现出参数不稳定性，从而在不存在扩散的情况下以强迫频率的一半在时间振荡中引起同步，并且在存在扩散的情况下出现时空模式临界阈值。我们制定了一个通用方案来分析得出临界阈值和色散关系，以定位振幅-频率图中倾斜的Arnold舌之间的不稳定空间模式。