Luo Chengjie, Zwicker David
Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
Phys Rev E. 2023 Sep;108(3-1):034206. doi: 10.1103/PhysRevE.108.034206.
Spatiotemporal patterns are often modeled using reaction-diffusion equations, which combine complex reactions between constituents with ideal diffusive motion. Such descriptions neglect physical interactions between constituents, which might affect resulting patterns. To overcome this, we study how physical interactions affect cyclic dominant reactions, like the seminal rock-paper-scissors game, which exhibits spiral waves for ideal diffusion. Generalizing diffusion to incorporate physical interactions, we find that weak interactions change the length- and time scales of spiral waves, consistent with a mapping to the complex Ginzburg-Landau equation. In contrast, strong repulsive interactions typically generate oscillating lattices, and strong attraction leads to an interplay of phase separation and chemical oscillations, like droplets co-locating with cores of spiral waves. Our work suggests that physical interactions are relevant for forming spatiotemporal patterns in nature, and it might shed light on how biodiversity is maintained in ecological settings.
时空模式通常使用反应扩散方程进行建模，该方程将成分之间的复杂反应与理想的扩散运动相结合。此类描述忽略了成分之间的物理相互作用，而这种相互作用可能会影响最终的模式。为了克服这一问题，我们研究物理相互作用如何影响循环主导反应，例如开创性的剪刀石头布游戏，该游戏在理想扩散情况下会呈现螺旋波。将扩散进行推广以纳入物理相互作用后，我们发现弱相互作用会改变螺旋波的长度和时间尺度，这与映射到复金兹堡 - 朗道方程一致。相比之下，强排斥相互作用通常会产生振荡晶格，而强吸引则会导致相分离和化学振荡的相互作用，例如液滴与螺旋波核心共定位。我们的工作表明，物理相互作用与自然界中时空模式的形成相关，并且可能有助于揭示生态环境中生物多样性是如何得以维持的。
