Alteration in Cross Diffusivities Governs the Nature and Dynamics of Spatiotemporal Pattern Formation

Abstract

Realizing spatiotemporal patterns out of a chemical reaction diffusion system remains an experimental challenge owing to the difficulty in overcoming the stringent condition of diffusion driven instability. Herein, by considering the spatially extended Gray‐Scott model system, we have investigated how the cross diffusivities of the reactants involved influence the nature and dynamics of spatiotemporal patterns. Our study unravels that in absence of diffusion driven instability, spatially inhomogeneous patterns can be obtained for the Gray‐Scott model system, and unstable time dependent patterns can be stabilized just by adjusting cross diffusivities of the reactants. Interestingly, the effect of cross diffusion in presence of the diffusion driven instability can differentially alter the speed of pattern formation, and potentially modify the nature of the spatiotemporal patterns obtained under different parametric conditions. Experimental verification of our findings may allow us to observe spatiotemporal patterns beyond the regime of classical Turing instability.

Spatial pattern of a class of SI models driven by cross diffusion

“…1952年, Turing [1] 发现在反应扩散系统中, 在 没有扩散的情况下对小时间扰动稳定的齐次稳态 在有扩散项的情况下变得不稳定, 这种现象被称 作Turing不稳定, 这种不稳定在空间域中产生了 一种称为Turing斑图的模式. 在这一发现之后, 许多研究者受到启发, 将Turing斑图应用于物 理、化学、生物和生态过程等各个领域 [2][3][4][5][6][7][8] . 反应扩散系统是空间运动建模的重要工具之 一, 已广泛应用于化学反应 [9] 、谣言传播 [10] 、图像 处理 [11] 、流行病传播 [12] 在流行病学领域, 研究人员提出了反应扩散模 型, Wang等 [13] 研究了包含人口与流行病过程的 反应扩散模型以捕捉环境的空间异质性和个体的 移动对疾病动态的影响.…”

Antiresonance and Stabilization in Spatio‐Temporal Dynamics of a Periodically Driven Gray‐Scott Reaction‐Diffusion System

“…To proceed further we consider the Gray-Scott [60][61][62][63][64][65][66] kinetics which is essentially a variant of the cubic auto-catalytic model of Glycolysis in an open flow reactor: U + 2 V! 3 V, V!P.Far from equilibrium condition is maintained by continuously supplying the reactant species U and removing the product P keeping surplus of U and V which allows a variety of instabilities and nonlinear dynamic phenomena to be unfolded.…”