Critical line in random-threshold networks with inhomogeneous thresholds
Critical line in random-threshold networks with inhomogeneous thresholds
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DOI：
10.1103/physreve.78.066118
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发表时间：
2008-12-01
影响因子：
2.4
通讯作者：
Rohlf, Thimo
中科院分区：
文献类型：
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作者：
Rohlf, Thimo
我们解析地计算了均匀和非均匀阈值下随机阈值网络（RTNs）的临界连通度K-c，并通过数值模拟验证了结果。我们发现K-c随（平均）绝对阈值的超线性增加|H|，其中K-c接近（|H|）类似于h（2）/（21 n| H|）对于大型|H|证明了这种渐近标度对于具有泊松分布连通性和阈值分布且方差增长慢于h（2）的RTN是普适的。有趣的是，我们发现，不均匀分布的阈值导致增加传播的扰动稀疏连接的网络，而密集连接的网络的损害减少;交叉点产生一个特征连接K-d，没有对应的布尔网络与过渡函数不限于阈值相关的开关。最后，引入节点阈值与入度的局部相关性。在这里，数值模拟表明，即使是弱的（反）相关性可以导致从有序到混沌动力学的过渡，反之亦然。
We calculate analytically the critical connectivity K-c of random-threshold networks (RTNs) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a superlinear increase of K-c with the (average) absolute threshold |h|, which approaches K-c(|h|) similar to h(2)/(21n|h|) for large |h|, and show that this asymptotic scaling is universal for RTNs with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than h(2). Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced; the crossover point yields a characteristic connectivity K-d, that has no counterpart in Boolean networks with transition functions not restricted to threshold-dependent switching. Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti) correlations can lead to a transition from ordered to chaotic dynamics, and vice versa.