Efficiency-Controllable Random Walks on a Class of Recursive Scale-Free Trees with a Deep Trap  

作　　者：李玲 关佶红 周水庚 

机构地区：[1]Department of Computer Science and Technology, Tongji University, Shanghai 201804 [2]Department of Basic Courses, Zhejiang Shuren University, Hangzhou 310015 [3]School of Computer Science, Fudan University, Shanghai 200433 [4]Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433

出　　处：《Chinese Physics Letters》2015年第3期13-16,共4页中国物理快报（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant Nos 61173118,61373036 and 61272254

摘　　要：Controls, especially effficiency controls on dynamical processes, have become major challenges in many complex systems. We study an important dynamical process, random walk, due to its wide range of applications for modeling the transporting or searching process. For lack of control methods for random walks in various structures, a control technique is presented for a class of weighted treelike scale-free networks with a deep trap at a hub node. The weighted networks are obtained from original models by introducing a weight parameter. We compute analytically the mean first passage time （MFPT） as an indicator for quantitatively measurinM the et^ciency of the random walk process. The results show that the MFPT increases exponentially with the network size, and the exponent varies with the weight parameter. The MFPT, therefore, can be controlled by the weight parameter to behave superlinearly, linearly, or sublinearly with the system size. This work provides further useful insights into controllinM eftlciency in scale-free complex networks.Controls, especially effficiency controls on dynamical processes, have become major challenges in many complex systems. We study an important dynamical process, random walk, due to its wide range of applications for modeling the transporting or searching process. For lack of control methods for random walks in various structures, a control technique is presented for a class of weighted treelike scale-free networks with a deep trap at a hub node. The weighted networks are obtained from original models by introducing a weight parameter. We compute analytically the mean first passage time （MFPT） as an indicator for quantitatively measurinM the et^ciency of the random walk process. The results show that the MFPT increases exponentially with the network size, and the exponent varies with the weight parameter. The MFPT, therefore, can be controlled by the weight parameter to behave superlinearly, linearly, or sublinearly with the system size. This work provides further useful insights into controllinM eftlciency in scale-free complex networks.

关 键 词：Efficiency-Controllable Random Walks on a Class of Recursive Scale-Free Trees with a Deep Trap 

分 类 号：O231[理学—运筹学与控制论] O157.5[理学—数学]