Functional relation between fluctuation and node degree in coupled stochastic dynamical systems

For the coupled stochastic dynamical system, we study the functional relation between noisy fluctuation and node degree. We extend the approaches for obtaining functional relation in Wang et al. (2009) to the weighted network whose link weight is dependent on the node degree. For the network with strong heterogeneity in degree distribution, we find that the theoretical result derived from the approaches in Wang et al. (2009) shows disagreement with numerical results. Here, we propose novel approaches using the average of higher order moments and improve the accuracy of functional relation between noisy fluctuation and node degree. Also, we investigate the functional relation of noisy fluctuation versus node input strength.