论文标题
网络上的非线性共识：均衡，有效的抗性和图案的树木
Nonlinear consensus on networks: equilibria, effective resistance and trees of motifs
论文作者
论文摘要
我们研究了无向网络的非线性动力学家族，从而概括了线性共识。我们根据网络的拓扑结构找到了其平衡点的紧凑表达，并使用配备有适当权重的基础图的有效电阻对其稳定性进行了分类。我们的一般结果应用于某些特定的网络，即树木，周期和完整的图。当两个子网的联合以一个节点连接到一个网络时，我们表明可以通过简单地研究较小的子网络来找到整个网络中的平衡点和稳定性。递归应用，该特性开辟了可能研究由图案树木制成的网络家族的动态行为的可能性。
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the effective resistance of the underlying graph equipped with appropriate weights. Our general results are applied to some specific networks, namely trees, cycles and complete graphs. When a network is formed by the union of two subnetworks joined in a single node, we show that the equilibrium points and stability in the whole network can be found by simply studying the smaller subnetworks instead. Applied recursively, this property opens the possibility to investigate the dynamical behaviour on families of networks made of trees of motifs.
