Dúzs Brigitta, Molnár István, Lagzi István, Szalai István
Institute of Chemistry, Eötvös L. University, 1117 Pázmány P. S. 1/A, Budapest 1117, Hungary.
Department of Physics and MTA-BME Condensed Matter Physics Research Group, Budapest University of Technology and Economics, 1111 Budafoki út 8, Budapest 1111, Hungary.
ACS Omega. 2021 Dec 10;6(50):34367-34374. doi: 10.1021/acsomega.1c04269. eCollection 2021 Dec 21.
Studying the effect of coupling and forcing of oscillators is a significant area of interest within nonlinear dynamics and has provided evidence of many interesting phenomena, such as synchronization, beating, oscillatory death, and phase resetting. Many studies have also reported along this line in reaction-diffusion systems, which are preferably explored experimentally by using open reactors. These reactors consist of one or two homogeneous (well-stirred) tanks, which provide the boundary conditions for a spatially distributed part. The spatiotemporal dynamics of this configuration in the presence of temporal oscillations in the homogeneous part has not been systematically investigated. This paper aims to explore numerically the effect of time-periodic boundary conditions on the dynamics of open reactors provided by autonomous and forced oscillations in the well-stirred part. A simple model of pH oscillators can produce various phenomena under these conditions, for example, superposition and modulation of spatiotemporal oscillations and forced bursting. The autonomous oscillatory boundary conditions can be generated by the same kinetic instabilities that result in spatiotemporal oscillations in the spatially distributed part. The forced oscillations are induced by sinusoidal modulation on the inflow concentration of the activator in the tank. The simulations confirmed that this type of forcing is more effective when the modulation period is longer than the residence time of the well-stirred part. The use of time-periodic boundary conditions may open a new perspective in the control and design of spatiotemporal phenomena in open one-side-fed and two-side-fed reactors.
研究振荡器的耦合和强迫作用是非线性动力学中一个重要的研究领域，并且已经为许多有趣的现象提供了证据，例如同步、拍频、振荡死亡和相位重置。许多沿着这条线的研究也报道了反应扩散系统，这些系统最好通过使用开放式反应器进行实验探索。这些反应器由一个或两个均匀（充分搅拌）的槽组成，它们为空间分布部分提供边界条件。在均匀部分存在时间振荡的情况下，这种配置的时空动力学尚未得到系统研究。本文旨在通过数值方法探索时间周期边界条件对由充分搅拌部分的自主振荡和强迫振荡提供的开放式反应器动力学的影响。一个简单的pH振荡器模型在这些条件下可以产生各种现象，例如时空振荡的叠加和调制以及强迫爆发。自主振荡边界条件可以由导致空间分布部分时空振荡的相同动力学不稳定性产生。强迫振荡是由对槽中激活剂流入浓度的正弦调制引起的。模拟证实，当调制周期长于充分搅拌部分的停留时间时，这种类型的强迫更有效。使用时间周期边界条件可能会为单侧进料和双侧进料开放式反应器中时空现象的控制和设计开辟一个新的视角。
