Blow-up in a p-Laplacian mutualistic model based on graphs

In this paper, we study a $p\,$-Laplacian ( p > 2 ) reaction-diffusion system based on weighted graphs that is used to describe a network mutualistic model of population ecology. After overcoming difficulties caused by the nonlinear $p\,$-Laplacian, we develop a new strong mutualistic condition, and the blow-up properties of the solution for any nontrivial initial data are proved under this condition. In this sense, we extend the blow-up results of models with a graph Laplacian ($p = 2$) to a general graph $p\,$-Laplacian

Understanding the Complexity of Temperature Dynamics in Xinjiang, China, from Multitemporal Scale and Spatial Perspectives

Based on the observed data from 51 meteorological stations during the period from 1958 to 2012 in Xinjiang, China, we investigated the complexity of temperature dynamics from the temporal and spatial perspectives by using a comprehensive approach including the correlation dimension (CD), classical statistics, and geostatistics. The main conclusions are as follows (1) The integer CD values indicate that the temperature dynamics are a complex and chaotic system, which is sensitive to the initial conditions. (2) The complexity of temperature dynamics decreases along with the increase of temporal scale. To describe the temperature dynamics, at least 3 independent variables are needed at daily scale, whereas at least 2 independent variables are needed at monthly, seasonal, and annual scales. (3) The spatial patterns of CD values at different temporal scales indicate that the complex temperature dynamics are derived from the complex landform

Dynamic Evolution of Securities Market Network Structure under Acute Fluctuation Circumstances

This empirical research applies cointegration in the traditional measurement method first to build directed weighted networks in the context of stock market. Then, this method is used to design the indicators and the value simulation for measuring network fluctuation and studying the dynamic evolution mechanism of stock market transaction networks as affected by price fluctuations. Finally, the topological structure and robustness of the network are evaluated. The results show that network structure stability is strong in the bull market stage and weak in the bear market stage. And the convergence rate of the dynamic evolution of network fluctuation is higher in the bull market stage than in the bear market stage

Asymptotic and transient dynamics of SEIR epidemic models on weighted networks

We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission

A free boundary problem for an attraction–repulsion chemotaxis system

Abstract In this paper we study an attraction–repulsion chemotaxis system with a free boundary in one space dimension. First, under some conditions, we investigate existence, uniqueness and uniform estimates of the global solution. Next, we prove a spreading–vanishing dichotomy for this model. In the vanishing case, the species fail to establish and die out in the long run. In the spreading case, we provide some sufficient conditions to prove that the species successfully spread to infinity as t→∞ $t\rightarrow\infty$ and stabilize at a constant equilibrium state. The criteria for spreading and vanishing are also obtained

Blow-up in a network mutualistic model

A graph Laplacian reaction–diffusion system is introduced to describe a network mutualistic model of population ecology. By the approach of upper and lower solutions, we show that the strong mutualistic system occurs blow-up if the intrinsic growth rates of population are large