网络上双稳态反应扩散系统的行波前沿和钉扎前沿
Traveling and pinned fronts in bistable reaction-diffusion systems on network
摘要：
双稳态反应扩散系统中的行波波前和定态局域斑图在经典连续介质和规则晶格中得到了广泛的研究。这种非平衡模式的类似物在网络中也是可能的。在这里，我们考虑随机Erdös-Rényi，无标度和分层树网络上的双稳态单组分系统的旅行和平稳模式。数值模拟结果表明，在网络组织的系统中存在着运动锋。它们代表了从一个稳定状态到另一个稳定状态的过渡波，在整个网络中传播。此外，前部可以被销接，从而形成固定结构。虽然之前已经考虑了扩散耦合双稳态元件链的前沿钉扎，但网络架构带来了显著的差异。节点的度（连接数）扮演着重要的角色。对于具有固定分支因子的正则树，给出了钉扎条件的解析表达式。对于大的Erdös-Rényi网络和无标度网络，构造了平稳模式的平均场论.
英文摘要：
Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
