论文标题
异构兴奋性系统在混合相变低于杂交相的阶段
Heterogeneous excitable systems exhibit Griffiths phases below hybrid phase transitions
论文作者
论文摘要
在$ d> 2 $中，均匀的阈值阈值模型不连续过渡发生，但是平均场解决方案提供了$ 1/t $ powerlaw活动衰减和其他幂律，因此称为混合订单或混合类型。最近已经显示，引入淬火障碍会出现不连续性和二阶相变和格里菲斯阶段。在这里，我们提供了数值证据，即使在高尺寸层次层次模块化网络的情况下，$ k = 2 $阈值模型的Griffith阶段也存在于混合相变的下方。这是由于模块通过单个链接连接的模块的活性传播的碎片。在阈值类型的异质系统的情况下，这提供了广泛的机制，为在扩展的Griffiths相位参数空间中发生动态关键性的大脑或流行病建模。我们在具有和没有抑制性联系的合成模块化网络以及难治状态的存在中研究了这一点。
In $d > 2$ dimensional, homogeneous threshold models discontinuous transition occur, but the mean-field solution provides $1/t$ power-law activity decay and other power-laws, thus it is called mixed-order or hybrid type. It has recently been shown that the introduction of quenched disorder rounds the discontinuity and second order phase transition and Griffiths phases appear. Here we provide numerical evidence, that even in case of high graph dimensional hierarchical modular networks the Griffiths phase of the $K=2$ threshold model is present below the hybrid phase transition. This is due to the fragmentation of the activity propagation by modules, which are connected via single links. This provides a widespread mechanism in case of threshold type of heterogeneous systems, modeling the brain or epidemics for the occurrence of dynamical criticality in extended Griffiths phase parameter spaces. We investigate this in synthetic modular networks with and without inhibitory links as well as in the presence of refractory states.
