Fan Weili, Ma Fengna, Tong Yuan, Liu Qian, Liu Ruoqi, He Yafeng, Liu Fucheng
College of Physics Science and Technology, Hebei University, Baoding 071002, People's Republic of China.
Hebei province Research Center for Basic disciplines of Computational Physics, Baoding 071002, People's Republic of China.
Phys Chem Chem Phys. 2023 Oct 4;25(38):26023-26031. doi: 10.1039/d3cp02464d.
One of the central issues in pattern formation is understanding the response of pattern-forming systems to an external stimulus. While significant progress has been made in systems with only one instability, much less is known about the response of complex patterns arising from the interaction of two or more instabilities. In this paper, we consider the effects of square spatial periodic forcing on oscillatory hexagon patterns in a two-layer coupled reaction diffusion system which undergoes both Turing and Hopf instabilities. Two different types of additive forcings, namely direct and indirect forcing, have been applied. It is shown that the coupled system exhibits different responses towards the spatial forcing under different forcing types. In the indirect case, the oscillatory hexagon pattern transitions into other oscillatory Turing patterns or resonant Turing patterns, depending on the forcing wavenumber and strength. In the direct forcing case, only non-resonant Turing patterns can be obtained. Our results may provide new insight into the modification and control of spatio-temporal patterns in multilayered systems, especially in biological and ecological systems.
模式形成中的核心问题之一是理解模式形成系统对外部刺激的响应。虽然在只有一种不稳定性的系统中已经取得了显著进展，但对于由两种或更多种不稳定性相互作用产生的复杂模式的响应却知之甚少。在本文中，我们考虑方形空间周期强迫对两层耦合反应扩散系统中振荡六边形模式的影响，该系统经历了图灵不稳定性和霍普夫不稳定性。应用了两种不同类型的加性强迫，即直接强迫和间接强迫。结果表明，在不同的强迫类型下，耦合系统对空间强迫表现出不同的响应。在间接情况下，振荡六边形模式会根据强迫波数和强度转变为其他振荡图灵模式或共振图灵模式。在直接强迫情况下，只能获得非共振图灵模式。我们的结果可能为多层系统中时空模式的修改和控制提供新的见解，特别是在生物和生态系统中。
