Derivation and characteristics of closed‐form solutions of the fundamental equations for online user dynamics
Derivation and characteristics of closed‐form solutions of the fundamental equations for online user dynamics
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DOI：
10.1002/cpe.6619
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发表时间：
2021-03
期刊：
影响因子：
--
通讯作者：
Toshi Ikeya;Masaki Aida
中科院分区：
文献类型：
--
作者：
Toshi Ikeya;Masaki Aida
基于网络波动方程的振荡模型可以描述在线社交网络中的用户动态。在振荡模型中引入用户动力学的基本方程，可以显式地描述特定网络结构产生的用户动力学的因果关系。此外，考虑到在线社交网络的链接结构的稀疏性，设计了一种新的不同形式的基本方程。在这篇文章中，我们导出了新基本方程的封闭形式解。此外，我们证明了新的基本方程的封闭形式的解决方案，可以产生原来的波动方程的通解，并调查派生的通解的特性。
The oscillation model, based on the wave equation on networks, can describe user dynamics in online social networks. The fundamental equation of user dynamics can be introduced into the oscillation model to explicitly describe the causal relation of user dynamics yielded by certain specific network structures. Moreover, by considering the sparseness of the link structure of online social networks, a novel fundamental equation of different forms has been devised. In this article, we derive a closed‐form solution of the new fundamental equation. Also, we show that the closed‐form solution of the new fundamental equation can generate the general solution of the original wave equation and investigate the characteristics of the derived general solution.