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Moreover, we also obtain equilibrium rather than oly free-disposal equilibrium under an additional standard condition.

此外,我们在增加一个标准条件下证得均衡存在,而不仅是自由处置均衡的存在性。

All equilibrium points of the original system are stable equilibrium points in the adjoint system.

对于一个非线性自治动力系统,存在一个伴随系统,该伴随系统是一个梯度系统,原始系统的所有平衡点都是伴随系统的渐近稳定平衡点,并且每一平衡点存在解析形式的Lyapunov函数。

For a nonlinear autonomous dynamic system, there exists an adjoint system, which is a gradient system. All equilibrium points of the original system are stable equilibrium points in the adjoint system.

对于一个非线性自治动力系统,存在一个伴随系统,该伴随系统是一个梯度系统,原始系统的所有平衡点都是伴随系统的渐近稳定平衡点,并且每一平衡点存在解析形式的Lyapunov函数。

Assignment Method Required Attributes Required Settings All or Nothing Time none Capacity Restraint Time Iterations Capacity Convergence Alpha Beta Incremental Time Iterations Capacity Convergence Alpha Beta User Equilibrium Time Iterations Capacity Convergence Alpha Beta Stochastic User Equilibrium Time Iterations Capacity Convergence Alpha Beta Function Error System Optimum Time Iterations Capacity Convergence Alpha Beta

表格格式乱了,就这么翻吧) 1。全有全无分配法。所需属性:时间;所需设置:无; 2。容量限制法。所需属性:时间,通行能力;所需设置:迭代,收敛,α,β; 3。增量分配法。所需属性:时间,通行能力;所需设置:迭代,收敛,α,β; 4。用户平衡法。所需属性:时间,通行能力;所需设置:迭代,收敛,α,β; 5。随机用户平衡法。所需属性:时间,通行能力;所需设置:迭代,收敛,α,β,函数,误差; 6。系统最佳法。所需属性:时间,通行能力;所需设置:迭代,收敛,α,β。

Choosing time delay as the control parameter, the stability of trivial equilibrium is discussed by analyzing distribution of the roots of the associated characteristic equation. It is found that Hopf bifurcation occurs from trivial equilibrium when the delay passes through critical values, then the critical values and their relations with system control parameters are obtained.

以时滞量为参数,通过分析对应线性系统特征方程的根的分布,讨论了平凡解的稳定性,得到了平凡解发生Hopf分岔而失稳的临界时滞量以及临界时滞量与系统控制参数的关系。

By the method in this paper, for deciding the global asymptotic stability of the equilibrium point, it is not necessary to verify whether the equilibrium point is unique and to construct Liyapunov functions.

由于非线性电路的复杂性,目前适合于该问题的方法,主要是LIYAPUNOV直接[13] 。应用LIYAPUNOV直接法分析电路的平衡点全局渐进稳定性,有两个基本的问题难以解决。

By the method in this paper,for deciding the global asymptotic stability of the equilibrium point,it is not necessary to verify whether the equilibrium point is unique and to construct Liyapunov functions.

与目前该问题所采用的LIYAPUNOV直接法相比,该方法具有无须判断平衡点的唯一性,判别方程直接明了等优点,电路维数越大时,本文的方法越有其优势。

It is proved that, when the value of critical threshold less than 1, the disease free equilibrium point is globally asymptotically stable. Further more, Bursaphelenchtis Xylophilus is used to construct the Lyapunov function, and the stability theory of Lyapunov function is used to prove that the equilibrium point is Global asymptotic stable. It explains that the Bursaphelenchus Xylophilus wiil eventually disappear.

证明了当临界阈值小于1时,无病平衡点是局部渐近稳定的,进一步利用巴尔巴欣公式构造Lyapunov函数,运用Lyapunov稳定性理论证明了该平衡点的全局渐近稳定性,说明松材线虫病会最终消失;当临界阈值大于1时,病虫害平衡点是局部渐近稳定的。

In order to investigate the influence of magnetic field on the vapor-liquid equilibrium of binary azeotrope,the vapor-liquid equilibrium of n-butanol-water system was studied under magnetic field with different magnetic induction intensity.

为探讨磁场对二元共沸物系汽液平衡的影响,在不同磁感应强度的磁场中,研究了正丁醇-水物系的汽液平衡。

Course Content: The Basic Laws of Thermodynamics, Thermodynamic Properties of Mass, Phases Equilibrium of One Gas System, Phases Equilibrium and Chemical Equilibrium of Gases System, Thermodynamics of Irreversible Processes, Description of Microstates, Boltzman Statistics, Bose-Einstein Statistics and Fermi-Dirac Statistics, Ensemble theory, The Statistical Theory and Fluctuation Theory for Nonequilibrium States

课程内容:热力学的基本定律、均匀物质的热力学性质、热动平衡判据、单元系的复相平衡、多元系的复相平衡和化学平衡、不可逆过程热力学、微观运动状态的描述、玻尔兹曼统计理论、玻色-爱因斯坦统计和费米-狄拉克统计理论、系综理论、非平衡态统计理论和涨落理论。

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