A Sharp Bound on the $s$-Energy and Its Applications to Averaging Systems
A Sharp Bound on the $s$-Energy and Its Applications to Averaging Systems
复制标题
$s$-能量的急剧界限及其在平均系统中的应用
DOI：
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发表时间：
2018
影响因子：
6.8
通讯作者：
B. Chazelle
中科院分区：
文献类型：
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作者：
B. Chazelle
<italic> <inline-formula> <tex-math notege =“ latex”> $ s $ </tex-math> </inline-formula> -Emergy </italic>是网络中广泛适用性的生成函数 - 基于动力学。
ho s）^{n-1} $ </tex-math> </inline-formula> <inline-formula> <tex-math notegy =“ latex”> $ s $ s $ </tex-math> </ inline-formula> <inline-formula> <tex-math notegy =“ latex”> $ n $ </tex-math> </inline-formula> - 代理对称平均系统-formula> <tex-math notegy =“ latex”> $ sleq 1 $ </tex-math> </inline-formula>，其中<inline-formula> <tex-math notegy =“ latex”> $
$ </tex-math> </inline-formula>是在非零的权重上的下限。在<inline-formula> <tex-math notegy =“ latex”> $ s $ </tex-math> </inline-formula> - 以增强舆论动态，羊群和同步系统中系统的收敛速率。
The <italic><inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula>-energy</italic> is a generating function of wide applicability in network-based dynamics. We derive an (essentially) optimal bound of <inline-formula><tex-math notation="LaTeX">$(3/
ho s)^{n-1}$</tex-math></inline-formula> on the <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula>-energy of an <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-agent symmetric averaging system, for any positive real <inline-formula><tex-math notation="LaTeX">$sleq 1$</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$
ho$</tex-math></inline-formula> is a lower bound on the nonzero weights. This is done by introducing the new dynamics of <italic>twist systems</italic>. We show how to use the new bound on the <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula>-energy to tighten the convergence rates of systems in opinion dynamics, flocking, and synchronization.