The recognition on the trend of wind energy stability is still extremely rare,although it is closely related to acquisition efficiency,grid connection,equipment lifetime,and costs of wind energy utilization.Using the ...The recognition on the trend of wind energy stability is still extremely rare,although it is closely related to acquisition efficiency,grid connection,equipment lifetime,and costs of wind energy utilization.Using the 40-year(1979–2018)ERA-Interim data from the European Center for Medium-Range Weather Forecasts,this study presented the spatial-temporal distribution and climatic trend of the stability of global offshore wind energy as well as the abrupt phenomenon of wind energy stability in key regions over the past 40 years with the climatic analysis method and Mann-Kendall(M-K)test.The results show the following 5 points.(1)According to the coefficient of variation(C_(v))of the wind power density,there are six permanent stable zones of global offshore wind energy:the southeast and northeast trade wind zones in the Indian,Pacific and Atlantic oceans,the Southern Hemisphere westerly,and a semi-permanent stable zone(North Indian Ocean).(2)There are six lowvalue zones for both seasonal variability index(S_(v))and monthly variability index(M_(v))globally,with a similar spatial distribution as that of the six permanent stable zones.M_(v) and S_(v) in the Arabian Sea are the highest in the world.(3)After C_(v),M_(v) and S_(v) are comprehensively considered,the six permanent stable zones have an obvious advantage in the stability of wind energy over other sea areas,with C_(v) below 0.8,M_(v) within 1.0,and S_(v) within 0.7 all the year round.(4)The global stability of offshore wind energy shows a positive climatic trend for the past four decades.C_(v),M_(v) and S_(v) have not changed significantly or decreased in most of the global ocean during 1979 to2018.That is,wind energy is flat or more stable,while the monthly and seasonal variabilities tend to shrink/smooth,which is beneficial for wind energy utilization.(5)C_(v) in the low-latitude Pacific and M_(v) and S_(v) in both the North Indian Ocean and the low-latitude Pacific have an obvious abrupt phenomenon at the end of the20th century.展开更多
In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equi...In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equilibria, and prove the global stability of them and the behaviour of the model when the basic reproduction ratio R0 is greater than one or less than one. The global stability of equilibria is established by using Lyapunov method. Graphical representations of the calculated parameters and their effects on disease eradication are provided.展开更多
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
The global asymptotic stability problem of Cellular neural networks with delay is investigated.A new stability condition is presented based on Lyapunov-Krasovskii method,which is dependent on the size of delay.The res...The global asymptotic stability problem of Cellular neural networks with delay is investigated.A new stability condition is presented based on Lyapunov-Krasovskii method,which is dependent on the size of delay.The result is given in the form of LMI,and the admitted upper bound of the delay can be obtained easily.The time delay dependent and independent results can be obtained,which include some results in the former literature.Finally,a numerical example is given to illustrate the effectiveness of the main results.展开更多
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obta...A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.展开更多
In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no end...In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.展开更多
The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of ...The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.展开更多
A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derive...A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.展开更多
In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch in...In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].展开更多
In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent lit...In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.展开更多
In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., ...In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.展开更多
In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By u...In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.展开更多
By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequ...By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.展开更多
In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model h...In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.展开更多
A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique,...A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.展开更多
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constru...Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.展开更多
In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global e...In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.展开更多
Recent research results indicate that individual awareness can play an important influence on epidemic spreading in networks. By local stability analysis, a significant conclusion is that the embedded awareness in an ...Recent research results indicate that individual awareness can play an important influence on epidemic spreading in networks. By local stability analysis, a significant conclusion is that the embedded awareness in an epidemic network can increase its epidemic threshold. In this paper, by using limit theory and dynamical system theory, we further give global stability analysis of a susceptible-infected-susceptible (SIS) epidemic model on networks with awareness. Results show that the obtained epidemic threshold is also a global stability condition for its endemic equilibrium, which implies the embedded awareness can enhance the epidemic threshold globally. Some numerical examples are presented to verify the theoretical results.展开更多
This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multipli...This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.展开更多
基金The Open Fund Project of Shandong Provincial Key Laboratory of Ocean EngineeringOcean University of China under contract No.kloe201901the Open Research Fund of State Key Laboratory of Estuarine and Coastal Research under contract No.SKLEC-KF201707。
文摘The recognition on the trend of wind energy stability is still extremely rare,although it is closely related to acquisition efficiency,grid connection,equipment lifetime,and costs of wind energy utilization.Using the 40-year(1979–2018)ERA-Interim data from the European Center for Medium-Range Weather Forecasts,this study presented the spatial-temporal distribution and climatic trend of the stability of global offshore wind energy as well as the abrupt phenomenon of wind energy stability in key regions over the past 40 years with the climatic analysis method and Mann-Kendall(M-K)test.The results show the following 5 points.(1)According to the coefficient of variation(C_(v))of the wind power density,there are six permanent stable zones of global offshore wind energy:the southeast and northeast trade wind zones in the Indian,Pacific and Atlantic oceans,the Southern Hemisphere westerly,and a semi-permanent stable zone(North Indian Ocean).(2)There are six lowvalue zones for both seasonal variability index(S_(v))and monthly variability index(M_(v))globally,with a similar spatial distribution as that of the six permanent stable zones.M_(v) and S_(v) in the Arabian Sea are the highest in the world.(3)After C_(v),M_(v) and S_(v) are comprehensively considered,the six permanent stable zones have an obvious advantage in the stability of wind energy over other sea areas,with C_(v) below 0.8,M_(v) within 1.0,and S_(v) within 0.7 all the year round.(4)The global stability of offshore wind energy shows a positive climatic trend for the past four decades.C_(v),M_(v) and S_(v) have not changed significantly or decreased in most of the global ocean during 1979 to2018.That is,wind energy is flat or more stable,while the monthly and seasonal variabilities tend to shrink/smooth,which is beneficial for wind energy utilization.(5)C_(v) in the low-latitude Pacific and M_(v) and S_(v) in both the North Indian Ocean and the low-latitude Pacific have an obvious abrupt phenomenon at the end of the20th century.
文摘In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equilibria, and prove the global stability of them and the behaviour of the model when the basic reproduction ratio R0 is greater than one or less than one. The global stability of equilibria is established by using Lyapunov method. Graphical representations of the calculated parameters and their effects on disease eradication are provided.
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.
文摘The global asymptotic stability problem of Cellular neural networks with delay is investigated.A new stability condition is presented based on Lyapunov-Krasovskii method,which is dependent on the size of delay.The result is given in the form of LMI,and the admitted upper bound of the delay can be obtained easily.The time delay dependent and independent results can be obtained,which include some results in the former literature.Finally,a numerical example is given to illustrate the effectiveness of the main results.
文摘A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.
基金This work is supported by the National Sciences Foundation of China (10471040)the Youth Science Foundations of Shanxi Province (20021003).
文摘In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.
文摘The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.
文摘A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.
基金supported by Japan Society for the Promotion of Science (Grant Scientific Research (c), No. 24540219 to the first author, JSPS Fellows, No.237213 to the second author, and No. 222176 to the third author)
文摘In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].
基金supported by Scientific Research(c),No.24540219 of Japan Society for the Promotion of Sciencesupported by Grant-in-Aid for Research Activity Start-up,No.25887011 of Japan Society for the Promotion of Science
文摘In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.
基金Supported by the National Natural Science Foundation of China(1 0 0 71 0 2 2 ) Mathematical TianyuanFoundation of China(TY1 0 0 2 6 0 0 2 - 0 1 - 0 5 - 0 3 ) Shanghai Priority Academic Discipline Foundation
文摘In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.
基金supported in part by JSPS Fellows,No.237213 of Japan Society for the Promotion of Science to the first authorthe Grant MTM2010-18318 of the MICINN,Spanish Ministry of Science and Innovation to the second authorScientific Research (c),No.21540230 of Japan Society for the Promotion of Science to the third author
文摘In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.
文摘By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.
文摘In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.
基金Supported by the Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institutethe Younger Foundation of Yantai University (SX06Z9)
文摘A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.
文摘Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.
基金supported by 973 Programs (No.2008CB317110)the Key Project of Chinese Ministry of Education (No.107098)+1 种基金Sichuan Province Project for Applied Basic Research (No.2008JY0052)the Project for Academic Leader and Group of UESTC
文摘In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.
基金supported by the National Natural Science Foundation of China(Grant Nos.61004101,11161013,and 61164020)the Natural Science Foundation of Guangxi Province,China(Grant Nos.2011GXNSFB018059 and 2013GXNSFAA019006)+2 种基金the 2012 Open Grant of Guangxi Key Lab of Wireless Wideband Communication and Signal Processing,Chinathe 2012 Open Grant of the State Key Laboratory of Integrated Services Networks of Xidian University,Chinathe Graduate Education Innovation Project of Guilin University of Electronic Technology,China(Grant No.GDYCSZ201472)
文摘Recent research results indicate that individual awareness can play an important influence on epidemic spreading in networks. By local stability analysis, a significant conclusion is that the embedded awareness in an epidemic network can increase its epidemic threshold. In this paper, by using limit theory and dynamical system theory, we further give global stability analysis of a susceptible-infected-susceptible (SIS) epidemic model on networks with awareness. Results show that the obtained epidemic threshold is also a global stability condition for its endemic equilibrium, which implies the embedded awareness can enhance the epidemic threshold globally. Some numerical examples are presented to verify the theoretical results.
基金Sponsored by the NNSF of China(11031003,11271066,11326158)a grant of Shanghai Education Commission(13ZZ048)Chinese Universities Scientific Fund(CUSF-DH-D-2013068)
文摘This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.