Gray-Scott模型中时空模式的控制
Control of spatiotemporal patterns in the Gray-Scott model
摘要：
研究了时滞反馈控制对反应扩散系统时空斑图的形成和发展的影响。不同类型的控制方案进行了研究，包括单物种，对角，和混合控制。这种方法有助于揭示不同的动力学制度，其中所产生的混沌状态或从行波。在时空混沌的情况下，控制可以稳定均匀的稳态或导致一个平凡的稳态和一个传播的行波之间的双稳态。此外，当基本状态是稳定的行波脉冲时，控制能够推进稳态图灵模式或产生上述双稳态区域。在每种情况下，稳定性边界被发现在控制强度和时间延迟的参数空间，数值模拟表明，对角控制无法控制时空混沌。
英文摘要：
This paper studies the effects of a time-delayed feedback control on the appearance and development of spatiotemporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species, diagonal, and mixed control. This approach helps to unveil different dynamical regimes, which arise from chaotic state or from traveling waves. In the case of spatiotemporal chaos, the control can either stabilize uniform steady states or lead to bistability between a trivial steady state and a propagating traveling wave. Furthermore, when the basic state is a stable traveling pulse, the control is able to advance stationary Turing patterns or yield the above-mentioned bistability regime. In each case, the stability boundary is found in the parameter space of the control strength and the time delay, and numerical simulations suggest that diagonal control fails to control the spatiotemporal chaos.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
