发表机构
Wenzhou Institute of the University of Chinese Academy of Sciences; University of Chinese Academy of Sciences; Universitat de Barcelona; Saha Institute of Nuclear Physics（中国科学院大学温州研究院; 中国科学院大学; 巴塞罗那大学; 萨哈核物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析含扩散与趋化作用的Selkov糖酵解反应-扩散模型，揭示两种线性不稳定性，发现趋化作用可作为非单调控制参数调控斑图形成与转变。
AI 中文摘要
我们研究了包含扩散及两物种间趋化相互作用的空间扩展Selkov糖酵解模型中的线性不稳定性与斑图形成。线性稳定性分析揭示了两种不同的分岔：零波矢、有限频率的Hopf分岔，会导致空间均匀振荡；以及带有鞍结分岔的有限波矢Turing不稳定性，会产生 stationary（定态）非均匀斑图。选定的波矢$k_c$对趋化作用的性质和强度敏感，且随趋化参数非单调变化，允许在均匀态和斑图态之间发生重入式转变。当趋化作用足够强，使两物种相互吸引或相互排斥时，会出现一种特殊的不稳定性：当趋化强度接近有限阈值时， preferred wavevector（优选波矢）发散。我们通过二维非线性偏微分方程的大量直接数值模拟（DNS）补充线性分析，DNS结果证实了预测的不稳定性及其非单调、重入式特征，还揭示了在合适参数下的空间均匀振荡态。定态斑图包括斑点，以及意外发现的稳定条纹。我们进一步发现由趋化强度和扩散率比控制的斑点与条纹形态间的转变。条纹态的稳定性与线性振幅方程一致，而斑点-条纹转变归因于线性稳定性之外的非线性效应。我们的结果表明，趋化作用可作为反应-扩散系统中不稳定性选择、波长选择、重入式斑图形成及非线性斑图形态的非单调控制参数。
英文摘要
We study linear instabilities and pattern formation in a spatially extended Selkov model for glycolysis with diffusion and chemotactic interactions between two species. Linear stability analysis reveals two distinct bifurcations: a zero-wavevector, finite-frequency Hopf bifurcation leading to spatially homogeneous oscillations, and a finite-wavevector Turing instability with a saddle-node bifurcation leading to stationary inhomogeneous patterns. The selected wavevector, $k_c$, depends sensitively on the nature and strength of chemotaxis and varies nonmonotonically with the chemotaxis parameters, allowing re-entrant transitions between homogeneous and patterned states. For sufficiently strong chemotaxis, when the two species mutually attract or mutually repel each other, an unusual instability emerges in which the preferred wavevector diverges as a finite threshold in chemotactic strength is approached. We complement the linear analysis with extensive direct numerical simulations (DNS) of the nonlinear partial differential equations in two dimensions. The DNS confirm the predicted instabilities and their nonmonotonic and re-entrant character, and also reveal spatially uniform oscillatory states for suitable parameters. The stationary patterns include spots and, unexpectedly, stable stripes. We further uncover transitions between spot and stripe morphologies controlled by chemotactic strength and diffusivity ratios. The stability of the striped states is consistent with linear amplitude equations, whereas the spot-stripe transition is attributed to nonlinear effects beyond linear stability. Our results demonstrate that chemotaxis can act as a nonmonotonic control parameter for instability selection, wavelength selection, re-entrant pattern formation, and nonlinear pattern morphology in reaction-diffusion systems.
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