时滞反馈控制下三维节能减排系统的稳定性分析

考虑三维节能减排系统,施加时滞反馈控制,建立反馈控制下的节能减排系统,求解平衡点,分析系统稳定性,得到出现Hopf分支的条件.利用中心流形定理和Poincare规范型方法讨论Hopf分支的性质,给定参数进行数值模拟,验证理论结果的有效性.     

Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system

Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluc-tuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratiodependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation.     

政府调控下的能源供需系统动力学分析

依据一个经济时期内能源需求、能源供应和政府调控之间相互依存、相互制约的演化关系为背景建立了一个新的能源供需模型.模型中引入市场自身调节的闽值,政府调控的阈值,政府调控对能源需求和能源供应的影响系数等参数,通过参数的调整,分析了政府调控在能源供需中的作用.通过平衡点稳定性、系统的耗散性、Lyapunov指数谱等的分析,研究了系统的基本动力学行为,利用数值模拟的方法给出了系统的动力演化行为;给出了模型中参数估计的方式,对模型所反映的现实意义进行了解释,给出了数值模拟结果,验证了理论分析的正确性.     

(2+1)维Kadomtsev-Petviashvili方程解的时空分岔

本文利用平衡点的平移和拓展的三波测试方法,着重讨论了(2+1)维KadomtsevPetviashvili方程所描述的动力系统的时空分岔问题,得到了一些新的、重要的结果.     

Oscillation for a class of diffusive hematopoiesis model with several arguments

By considering solution curve's or surface's composition of the functions of several variables and constructing the suitable lower-upper solution pair for the following special diffusive Hematopoiesis model eP (t, x)/et= ΔP (t, x)- γP (t, x) +m Σi=1 βiP (t-τi,x)/1+Pn (t-τi,x) (0.1)under Neumann boundary condition, sufficient conditions are provided for the oscillation of the positive equilibrium for (0.1). Moreover, these results extend or complement existing results.     

Two-group SIR epidemic model with stochastic perturbation

A stochastic two-group SIR model is presented in this paper.The existence and uniqueness of its nonnegative solution is obtained,and the solution belongs to a positively invariant set.Furthermore,the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 ≤ 1,which means the disease will die out.While if R0 1,we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average.In addition,the intensity of the fluctuation is proportional to the intensity of the white noise.When the white noise is small,we consider the disease will prevail.At last,we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.     

一个新的四维节能减排系统的动力学分析及其控制

依据一个经济时期内节能减排、碳排放、经济增长和新能源的开发利用之间相互依存、相互制约的演化关系建立了一个新的四维节能减排动态演化模型,这是一类新的非线性微分系统,通过平衡点稳定性、系统的耗散性、Lyapunov指数谱等的分析,研究了系统的基本动力学行为,利用数值模拟的方法给出了系统的动力演化行为;利用线性反馈控制方法将四维节能减排系统的混沌态控制到原先不稳定的平衡点,给出了数值模拟结果,验证了理论分析的正确性.     

一类SIRS 传染病模型的新Lyapunov 函数

通过建立新的Lyapunov 函数研究了两类SIRS 传染病动力学模型,得到了两类模型的地方病平衡点的全局渐近稳定性。所得结果分别改进了文献[1,2]中的相关结论。     

一类传染病模型无病平衡点的全局稳定性

过去的半个多世纪,传染病模型在数学生态学领域已受广泛重视.研究了一个具时滞和扩散的传染病模型,重点讨论了该模型解的定性性质和稳态解的渐近行为;利用线性化和特征值方法讨论了正稳态解的局部稳定性,通过构造单调迭代序列,给出了正稳态解的全局稳定性. 最后给出了数值模拟和讨论,当接触率充分小时,问题的无病平衡点是全局渐近稳定的.     

Belousov Zhabotinsky化学反应系统的渐近稳定性

用无穷维动力系统的方法研究了Belousov Zhabotinsky化学反应系统的长时间行为.在齐次边界条件与非齐次边界条件下证明了系统在其不变流形上的全局吸引子为系统在该不变流形内的唯一平衡点,从而得到了该系统的渐近稳定性.