转换机制下具有非线性扰动的随机SIVS传染病模型的定性分析

该文考虑随机环境因素的影响,建立了一类转换机制下具有非线性扰动的SIVS模型.对于具有白噪声的非自治随机SIVS流行病系统,给出了解的随机有界性和随机持久性的结果,并利用李雅普诺夫函数和Has' minskii周期解理论证明了非平凡正周期解的存在性.对于具有马尔科夫变换的系统,建立了遍历平稳分布的充分条件,分别得到了染...     

Wick型随机广义Burgers方程的确切解

借助白噪声分析、Hermite变换和扩展的双曲函数法,研究了Wick型随机广义Burgers'方程,求出了一些精确的Wick型孤立波解和周期波解.由于Wick型函数难以赋值,为此,我们得到一些特殊情形下的Wick型随机广义Burgers'方程的非Wick型解.     

无穷维随机微分方程的渐近概周期解

该文引入了渐近θ-概周期随机过程的概念,并在算子半群理论框架下研究了一类带有渐近概周期系数的无穷维随机微分方程,利用随机分析理论建立了此类随机微分方程渐近θ-概周期解的存在性.此外该文还引入了依路径分布渐近概周期过程的概念,并证明了上述渐近θ-概周期解还是依路径分布渐近概周期的.值得注意的是,在早期的研究结果中,建立的均是更弱的一维分布渐近概周期解的存在性.     

随机哈密尔顿系统的周期变差解和近不变环面解

本文研究具有随机扰动的哈密顿系统的重现现象,尤其是轨道随机周期变差解和近不变环面解.具体来说,对线性薛定谔方程,我们完整阐述了随机周期变差解何时存在;对随机扰动的近可积哈密顿系统,我们证明了近不变环面的存在性与驱动噪声对应的哈密顿函数的对合性相关.     

Poincaré非线性振动理论在连续介质力学中的推广(Ⅱ)——若干应用

文本是文[1]的继续.文[1]中,提出和建议使用非线性偏微分方程直接摄动与加权积分方程法,计算连续介质系统的共振与非共振周期解.本文中,应用该方法计算了定跨度弹性梁在各种常见边界条件下强迫振动的共振与非共振周期解,方板在集中周期荷载作用下的共振周期解.指出了,非主振型对非线性振动周期解的影响及静荷载对幅频特性曲线的影响.     

强迫摆型碰撞振子的弹性周期解

本文考虑一类具有强迫力的摆型碰撞振子无穷多次调和的弹性周期解的存在性.通过坐标变换的方法把碰撞系统转化为定义在全平面上的等价系统,再运用相平面分析的方法对变换后系统的解的动力行为进行分析,通过在改进的Poincar映射上应用Poincar-Birkhoff扭转定理得到了无穷多次调和的弹性周期解的存在性.     

乘法需求模式下具有风险厌恶零售商的供应链合作博弈分析

考虑了一个风险中性的制造商和一个风险厌恶型零售商的供应链合作博弈问题.零售商面临依赖于价格的随机市场需求.以条件在险价值(CVaR)作为零售商的风险衡量准则,并采用乘法需求模式表示依赖于价格的随机需求.通过研究在乘法需求模式下具有不同协商权利的Nash博弈问题的最优均衡行为,从而发现平均需求函数为单调递减的凹函数是存在稳定均衡解的充分条件,且稳定均衡解存在与否与随机需求噪声的分布情况,零售商的协商权利都无关.在此前提下,发现在乘法需求模式下当需求噪声服从均匀分布时制造商占整个供应链的利润比例和一般随机需求情况下的一样,且随零售商的风险态度递增,与平均需求的函数形式无关.     

一类含强迫项的Rayleigh型方程的反周期解

利用双线性形式和重合度理论,研究了一类含有强迫项的Rayleigh曲型方程的反周期解,给出了反周期解存在和唯一的新的判据,所得结果改善了已有的工作.     

一类哈密顿系统周期函数的单调性

哈密顿函数H(x,y)=F(x)+G(y)所对应的哈密顿系统.给出了这类系统的周期解的周期为单调函数的几个充分条件,并用所得结果讨论了Volterral-Lotka系统和无阻尼、无强迫Duffing方程周期解周期的单调性.     

二维浅水波方程的间断周期解和间断孤立波解讨论

本文讨论地球流体运动浅水波模式中间断周期解与间断孤立波解.在系统的非平衡点即奇点附近考虑轨线性质时,我们发现只要引入广义解的概念(分片光滑连续解),就会产生间断周期解并得到了间断周期解的条件.当系统在退化的过程中,发现系统此时会产生间断的孤立波解,与此同时其它物理量也产生了间断.这里我们发现,一般认为在超高速情况下解会产生间断,然而在非超高速时也会产生间断现象.本文讨论了上述一系列问题得到了间断解的解析解表达式,并把这一事实与飑线的实例进行比较,得到了不少类似之处.     

海-气耦合气候系统非线性扰动模式的周期正解

与ENSO相关的热带大尺度海-气相互作用是影响全球气候年际变化的主要过程之一.该文从一个海-气相互作用方程组出发,推广了一个具有一般形式的海 气耦合气候系统非线性扰动模式.运用拓扑度理论,从数学上严格证明了一定条件下该模式存在周期正解的结果,并分析了所得结果潜在的应用价值.海-气相互作用研究,有助于理解气候变化过程,为气候模拟和预报提供理论基础.     

Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white noises. Some further developments, problems, and challenges in this direction are also discussed.     

Periodic Solution and Stationary Distribution of Stochastic Predator–Prey Models with Higher-Order Perturbation

In this paper, two stochastic predator–prey models with general functional response and higher-order perturbation are proposed and investigated. For the nonautonomous periodic case of the system, by using Khasminskii’s theory of periodic solution, we show that the system admits a nontrivial positive T-periodic solution. For the system disturbed by both white and telegraph noises, sufficient conditions for positive recurrence and the existence of an ergodic stationary distribution to the solutions are established. The existence of stationary distribution implies stochastic weak stability to some extent.     

Weak Solutions for Stochastic FitzHugh–Nagumo Equations

This article studies the existence of weak solutions for a stochastic version of the FitzHugh–Nagumo equations. The random elements are introduced through initial values and forcing terms of associated Cauchy problem, which may be white noise in the time. Moreover there is a dependence of a stochastic parameter.     

随机的改进Lotka-Volterra竞争模型

本文提出且讨论了一类两种群随机的改进Lotka Volterra竞争模型.白噪声及有色噪声都在本文中被考虑.我们得到了全局唯一正解、随机有界性、随机持久和随机灭绝等种群动力性质的充分条件.     

Equations stochastiques du type Navier-Stokes

We consider the problem of existence of solutions for stochastic Navier-Stokes equations. The random elements are the initial value of the solution and forcing terms which may be white noise in time.The method uses results on multi-valued functions. We also give energy type results and present examples.     

Stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

This paper addresses a stochastic SIS epidemic model with vaccination under regime switching. The stochastic model in this paper includes white and color noises. By constructing stochastic Lyapunov functions with regime switching, we establish sufficient conditions for the existence of a unique ergodic stationary distribution.     

A random attractor for a stochastic second order lattice system with random coupled coefficients

In this paper, we mainly focus on the asymptotic behavior of solutions to the second-order stochastic lattice equations with random coupled coefficients and multiplicative white noises in weighted spaces of infinite sequences. We first transfer stochastic lattice equations into random lattice equations and prove the existence and uniqueness of solutions which generate a random dynamical system. Second we consider the existence of a tempered random bounded absorbing set and a random attractor for the system. Then we establish the upper semicontinuity of random attractors as the coefficient of the white noise term tends to zero. Finally we present the corresponding results for the system with additive white noises.     

Random attractor for stochastic second-order non-autonomous stochastic lattice equations with dispersive term

In this paper, we consider the asymptotic behaviour of solutions to second-order non-autonomous stochastic lattice equations with dispersive term and additive white noises in the space of infinite sequences. We first transfer the stochastic lattice equations into random lattice equations, and prove the existence and uniqueness of solutions that generate a random dynamical system. Second, we prove the existence of a tempered random absorbing set and a random attractor for the system. Finally, we establish the upper semi-continuity of the random attractors as the coefficient of the white noise term tends to zero.     

Local Existence and Uniqueness for a Two-Dimensional Surface Growth Equation with Space-Time White Noise

We study local existence and uniqueness for a surface growth model with space-time white noise in 2D. Unfortunately, the direct fixed-point argument for mild solutions fails here, as we do not have sufficient regularity for the stochastic forcing. Nevertheless, one can give a rigorous meaning to the stochastic PDE and show uniqueness of solutions in that setting. Using spectral Galerkin method and any other types of regularization of the noise, we obtain always the same solution.