This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by ...This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.展开更多
针对传统数值预报模式计算时间长和计算资源消耗大的问题,以及现有深度学习预报方法在温度预报结果上不精确,且预测结果模糊的问题,提出了一个新的温度预报模型。首先,设计了一个时空信息捕捉模块,将该模块捕获的长期依赖信息,作为扩散...针对传统数值预报模式计算时间长和计算资源消耗大的问题,以及现有深度学习预报方法在温度预报结果上不精确,且预测结果模糊的问题,提出了一个新的温度预报模型。首先,设计了一个时空信息捕捉模块,将该模块捕获的长期依赖信息,作为扩散模型的生成条件,赋予扩散模型预报的能力;其次,设计了一个新的平衡损失函数,同时保护了扩散模型的生成能力和时空信息捕捉模块对时空信息的捕捉能力;最后,基于美国国家环境预报中心的再分析数据进行预报,与现有的深度学习方法相比,所提模型预报结果的质量在均方误差(mean square error,MSE)上降低了17.3%,在均方根误差(root mean square error,RMSE)上降低了9.14%,在峰值信噪比(peak signal to noise ratio,PSNR)上提升了5.1%。改进的扩散模型能有效地捕捉时空依赖的关系,有效地进行时空序列预测,效果优于其他对比方法。展开更多
In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the...In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.展开更多
建立了一类含分布时滞的革新传播模型(dU(t))/(dt)=-(α+βA(t))U(t)-ρU(t)+ρ,(dA(t))/(dt)=integral from 0 to (+∞)αE(τ)U(t-τ)dr+βu(t)A(t)-(ρ+κ)A(t).研究了分布时滞对传播过程的影响,讨论了正平衡点的存在性和唯一性及其...建立了一类含分布时滞的革新传播模型(dU(t))/(dt)=-(α+βA(t))U(t)-ρU(t)+ρ,(dA(t))/(dt)=integral from 0 to (+∞)αE(τ)U(t-τ)dr+βu(t)A(t)-(ρ+κ)A(t).研究了分布时滞对传播过程的影响,讨论了正平衡点的存在性和唯一性及其局部与全局的渐近稳定性.当分布时滞的核函数取δe^(-δτ)时,证明了正平衡点是绝对渐近稳定的.展开更多
基金supported by the NSFC Grant(No.11171158)Project of Graduate Education Innovation of Jiangsu Province(No.KYLX 0719)Project of Natural Science Research of Higher Education Institutions of Jiangsu Province(No.15KJB110008)
文摘This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.
文摘针对传统数值预报模式计算时间长和计算资源消耗大的问题,以及现有深度学习预报方法在温度预报结果上不精确,且预测结果模糊的问题,提出了一个新的温度预报模型。首先,设计了一个时空信息捕捉模块,将该模块捕获的长期依赖信息,作为扩散模型的生成条件,赋予扩散模型预报的能力;其次,设计了一个新的平衡损失函数,同时保护了扩散模型的生成能力和时空信息捕捉模块对时空信息的捕捉能力;最后,基于美国国家环境预报中心的再分析数据进行预报,与现有的深度学习方法相比,所提模型预报结果的质量在均方误差(mean square error,MSE)上降低了17.3%,在均方根误差(root mean square error,RMSE)上降低了9.14%,在峰值信噪比(peak signal to noise ratio,PSNR)上提升了5.1%。改进的扩散模型能有效地捕捉时空依赖的关系,有效地进行时空序列预测,效果优于其他对比方法。
基金supported by the National Natural Science Foundation of China (No.12231008 and No.11971185)。
文摘In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.
文摘建立了一类含分布时滞的革新传播模型(dU(t))/(dt)=-(α+βA(t))U(t)-ρU(t)+ρ,(dA(t))/(dt)=integral from 0 to (+∞)αE(τ)U(t-τ)dr+βu(t)A(t)-(ρ+κ)A(t).研究了分布时滞对传播过程的影响,讨论了正平衡点的存在性和唯一性及其局部与全局的渐近稳定性.当分布时滞的核函数取δe^(-δτ)时,证明了正平衡点是绝对渐近稳定的.
