A p-Laplacian ( p > 2 ) reaction-diffusion system on weighted graphs is introduced to a networked SIR epidemic model. After overcoming difficulties caused by the nonlinear p-Laplacian, we show that the endemic equi...A p-Laplacian ( p > 2 ) reaction-diffusion system on weighted graphs is introduced to a networked SIR epidemic model. After overcoming difficulties caused by the nonlinear p-Laplacian, we show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number r<sub>0</sub> is greater than 1, while the disease-free equilibrium is globally asymptotically stable if r<sub>0</sub> is lower than 1. We extend the stability results of SIR models with graph Laplacian ( p = 2 ) to general graph p-Laplacian.展开更多
In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mut...In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.展开更多
The complex network theory provides an approach for understanding the complexity of climate change from a new perspective.In this study,we used the coarse graining process to convert the data series of daily mean temp...The complex network theory provides an approach for understanding the complexity of climate change from a new perspective.In this study,we used the coarse graining process to convert the data series of daily mean temperature and daily precipitation from 1961 to 2011 into symbol sequences consisting of five characteristic symbols(i.e.,R,r,e,d and D),and created the temperature fluctuation network(TFN)and precipitation fluctuation network(PFN)to discover the complex network characteristics of climate change in the Tarim River Basin of Northwest China.The results show that TFN and PEN both present characteristics of scale-free network and small-world network with short average path length and high clustering coefficient.The nodes with high degree in TFN are RRR,d RR and Re R while the nodes with high degree in PFN are rre,rrr,eee and err,which indicates that climate change modes represented by these nodes have large probability of occurrence.Symbol R and r are mostly included in the important nodes of TFN and PFN,which indicate that the fluctuating variation in temperature and precipitation in the Tarim River Basin mainly are rising over the past 50 years.The nodes RRR,DDD,Re R,RRd,DDd and Ree are the hub nodes in TFN,which undertake 19.71%betweenness centrality of the network.The nodes rre,rrr,eee and err are the hub nodes in PFN,which undertake 13.64%betweenness centrality of the network.展开更多
Based on observational data obtained from 1961 to 2011 in the Tarim River Basin,China,we investigated the chaotic dynamics of temperature,precipitation,relative humidity,and evaporation.The main findings are as follow...Based on observational data obtained from 1961 to 2011 in the Tarim River Basin,China,we investigated the chaotic dynamics of temperature,precipitation,relative humidity,and evaporation.The main findings are as follow:(1)The four data series have significant chaotic and fractal behaviors,which are the result of the evolution of a nonlinear chaotic dynamic system.The climatic process in the Tarim River Basin also has deterministic and stochastic characteristics.(2)To describe the temperature,precipitation,relative humidity,and evaporation dynamics,at least three independent variables at daily scale are required;in terms of complexity,their order is evaporation>temperature>precipitation>relative humidity.(3)Their respective largest Lyapunov exponentλ1 shows the order of their degree of complexity is relative humidity>temperature>precipitation≈evaporation;the maximum time scales for which the four systems can be predicted are 17 days,17 days,16 days,and 16 days,if calculated separately.(4)The Kolmogorov entropy K illustrates that the complexity of the nonlinear precipitation system is much greater than that of the other three systems.Both temperature and evaporation systems exhibit weaker chaotic behavior,their predictability is better,and the degree of complexity is less than that of the other two factors.展开更多
文摘A p-Laplacian ( p > 2 ) reaction-diffusion system on weighted graphs is introduced to a networked SIR epidemic model. After overcoming difficulties caused by the nonlinear p-Laplacian, we show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number r<sub>0</sub> is greater than 1, while the disease-free equilibrium is globally asymptotically stable if r<sub>0</sub> is lower than 1. We extend the stability results of SIR models with graph Laplacian ( p = 2 ) to general graph p-Laplacian.
基金partially supported by National Natural Science Foundation of China(11771380)Natural Science Foundation of Jiangsu Province(BK20191436).
文摘In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.
基金supported by the Science and Technology Project of Jiangxi Provincial Department of Education (No. GJJ161097)the Open Foundation of the State Key Laboratory of Desert and OasisEcology (No. G2014-02-07)+2 种基金the National Natural Science Foundation of China (41630859)the Open Research Fund of Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing (No. 2016WICSIP012)the Key Project of Jiangxi Provincial Department of Science and Technology (No. 20161BBF60061)
文摘The complex network theory provides an approach for understanding the complexity of climate change from a new perspective.In this study,we used the coarse graining process to convert the data series of daily mean temperature and daily precipitation from 1961 to 2011 into symbol sequences consisting of five characteristic symbols(i.e.,R,r,e,d and D),and created the temperature fluctuation network(TFN)and precipitation fluctuation network(PFN)to discover the complex network characteristics of climate change in the Tarim River Basin of Northwest China.The results show that TFN and PEN both present characteristics of scale-free network and small-world network with short average path length and high clustering coefficient.The nodes with high degree in TFN are RRR,d RR and Re R while the nodes with high degree in PFN are rre,rrr,eee and err,which indicates that climate change modes represented by these nodes have large probability of occurrence.Symbol R and r are mostly included in the important nodes of TFN and PFN,which indicate that the fluctuating variation in temperature and precipitation in the Tarim River Basin mainly are rising over the past 50 years.The nodes RRR,DDD,Re R,RRd,DDd and Ree are the hub nodes in TFN,which undertake 19.71%betweenness centrality of the network.The nodes rre,rrr,eee and err are the hub nodes in PFN,which undertake 13.64%betweenness centrality of the network.
基金supported by the China Postdoctoral Science Foundation(2016M600515)Postdoctoral Preferred Fund of Jiangxi Province(2017KY48)+5 种基金the Jiangxi Postdoctoral Daily Fund Project(2016RC25)the Opening Fund of Key Laboratory of Poyang Lake Wetland and Watershed Research(Jiangxi Normal University)Ministry of Education(PK2017002)the Open Research Fund of Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing(2016WICSIP012)the National Natural Science Foundation of China(61703199)the Science and Technology Research Project of Jiangxi Provincial Education Department(GJJ180926)
文摘Based on observational data obtained from 1961 to 2011 in the Tarim River Basin,China,we investigated the chaotic dynamics of temperature,precipitation,relative humidity,and evaporation.The main findings are as follow:(1)The four data series have significant chaotic and fractal behaviors,which are the result of the evolution of a nonlinear chaotic dynamic system.The climatic process in the Tarim River Basin also has deterministic and stochastic characteristics.(2)To describe the temperature,precipitation,relative humidity,and evaporation dynamics,at least three independent variables at daily scale are required;in terms of complexity,their order is evaporation>temperature>precipitation>relative humidity.(3)Their respective largest Lyapunov exponentλ1 shows the order of their degree of complexity is relative humidity>temperature>precipitation≈evaporation;the maximum time scales for which the four systems can be predicted are 17 days,17 days,16 days,and 16 days,if calculated separately.(4)The Kolmogorov entropy K illustrates that the complexity of the nonlinear precipitation system is much greater than that of the other three systems.Both temperature and evaporation systems exhibit weaker chaotic behavior,their predictability is better,and the degree of complexity is less than that of the other two factors.
