Partial differential equation modeling with Dirichlet boundary conditions on social networks

Abstract

The being a wide range of applications of the Internet, social networks have become an effective and convenient platform for information communication, propagation and diffusion. Most of information exchange and spreading exist in social networks. The issue of information diffusion in social networks is getting more and more attention by government and individuals. The researchers investigated either empirical studies or focused on ordinary differential equation (ODE) models with only consideration of temporal dimension in most prior work. As is well known, partial differential equations (PDEs) can describe temporal and spatial patterns of information diffusion over online social networks; however, until now, results for understanding information propagation of social networks over both temporal and spatial dimensions are few. This paper is devoted to investigating a non-autonomous diffusive logistic model with Dirichlet boundary conditions to describe the process of information propagation in social networks. By constructing upper and lower solutions we obtain the dynamic behavior of the solution to the non-autonomous diffusive logistic model. Our results show that information diffusion is greatly affected by the diffusion coefficient d(t) and the intrinsic growth rate r(t).

A graph-theoretic method to study the existence of periodic solutions for a coupled Rayleigh system via inequality techniques

“…Up to now, the global existence of periodic solutions for differential systems has been investigated mainly by employing the following five methods: (1) Fixed point theorem methods [26]; (2) Combining continuation theorem of coincidence degree theory with the a priori estimate of periodic solutions [9,11,[13][14][15][27][28][29][30]; (3) Combining continuation theorem of coincidence degree theory with LMI [12]; (4) Combining continuation theorem of coincidence degree theory with Lyapunov function method [16,[18][19][20][21]31]; (5) The method of upper and lower functions. But, in the above-mentioned methods, (3) and (4) are used in recent years to study the existence of periodic solutions for different systems.…”

Regional Influenza Prediction with Sampling Twitter Data and PDE Model

“…Recently, the surveillance, monitoring, and analysis of epidemic outbreaks and spread via large-scale social media data have become an important and practical tool for government agencies and public health organizations to control and prevent the flu from spreading [2,[11][12][13][14][15][16]. Among these studies, a few efforts focus on flu twitter data itself, for instance for explicitly modeling the distinction between flu awareness and real flu infection [11,12].…”

“…This provides a rich set of high-quality datasets for efficient forecasting, while some studies apply a temporal topic model [13,14] or machine learning method [15,[17][18][19] to estimate the flu trends. Recently, a few mathematical models such as partial differential equation (PDE)-based approaches are proposed to predict the information diffusion over online social networks [16,20,21]. However, based on the data from social networks, all the existing PDE models referred above are built without consideration human activity.…”

Anti-periodic solutions problem for inertial competitive neutral-type neural networks via Wirtinger inequality

“…The Wirtinger inequality was first used in Fourier analysis, then was used in 1904 to prove the isoperimetric inequality; see [1,2]. Since the Wirtinger inequality has been recognized as a powerful tool to estimate the prior bounds of solutions, it has been used in many research areas, such as Hamiltonian system, delay equations, biomathematics, neural networks, partial differential equation; see [3][4][5][6][7][8] and the relevant references therein.…”