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Stationary patterns in star networks of bistable units: theory and application to chemical reactions

机译:双稳态单元星型网络中的平稳模式:理论和对化学反应的应用

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摘要

We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of the activations; such analysis enables the characterization of the formation of stationary patterns of localized activity. The results are interpreted with a theoretical analysis of a simplified bistable reaction-diffusion model. Weak coupling results in trivial pinned states where the activation cannot propagate. At strong coupling, a uniform state is expected with active or inactive elements at small or large degree networks, respectively. A nontrivial stationary spatial pattern, corresponding to an activation pinning, is predicted to occur at an intermediate number of peripheral elements and at intermediate coupling strengths, where the central activation of the network is pinned, but the peripheral activation propagates toward the center. The results are confirmed in experiments with star networks of bistable electrochemical reactions. The experiments confirm the existence of the stationary spatial patterns and the dependence of coupling strength on the number of peripheral elements for transitions between pinned and retreating or spreading fronts in forced network configurations (where the central or periphery elements are forced to maintain their states).
机译:我们目前在星型网络配置中耦合双稳态动力学单元的模式形成的理论和实验研究。通过对中心或外围元素应用局部扰动,我们演示了激活的后续扩展,固定或缩回。这样的分析能够表征局部活动的固定模式的形成。通过简化的双稳态反应扩散模型的理论分析来解释结果。弱耦合会导致激活无法传播的琐碎固定状态。在强耦合下,期望在小或大度网络上分别用活动或不活动元素形成均匀状态。预测会在中间数量的外围元素和中间耦合强度下发生与激活钉扎相对应的非平凡的固定空间模式,在该处,网络的中心激活被钉扎,但是外围激活会向中心传播。在双稳态电化学反应的星形网络的实验中证实了该结果。实验证实了在固定网络配置(其中中央或外围元素被迫保持其状态)中固定和退缩或扩展前沿之间过渡时,固定空间模式的存在以及耦合强度对外围元素数量的依赖性。

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