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广义Birkhoff系统动力学的一类逆问题 总被引：3，自引：0，他引：3
针对广义Birkhoff系统动力学,提出广义Birkhoff系统动力学的一类逆问题,研究由已知积分流形来建立广义Birkhoff方程. 这类逆问题的解通常不是唯一的,需给出必要的补充要求. 最后举例说明结果的应用.关键词：广义Birkhoff系统动力学逆问题积分流形 相似文献
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广义Birkhoff系统与一类组合梯度系统 总被引：1，自引：0，他引：1
提出一类组合梯度系统, 即将梯度系统与斜梯度系统相加而组成的一个系统, 并研究组合梯度系统的重要性质. 将广义Birkhoff系统在一定条件下化成组合梯度系统, 并利用组合梯度系统的性质来研究广义Birkhoff系统的积分和稳定性. 相似文献
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研究一类广义Birkhoff系统的广义正则变换.建立这类广义Birkhoff系统的运动微分方程,得到了该系统的广义正则变换以及保持广义正则变换的条件.最后,举例说明结果的应用. 相似文献
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将Birkhoff方程添加一附加项成为广义Birkhoff方程.将Birkhoff方程的一类积分推广并应用于广义Birkhoff方程.举例说明结果的应用.关键词：Birkhoff方程广义Birkhoff方程积分 相似文献
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广义Birkhoff系统的Birkhoff对称性与守恒量 总被引：1，自引：0，他引：1
研究广义Birkhoff系统的Birkhoff对称性问题,并给出此情形下相应的守恒量.将力学系统的等效Lagrange函数的一个定理推广到广义Birkhoff系统,证明了在一定条件下与两组动力学函数B,Rμ,Λμ和B,Rμ,Λμ分别给出的广义Birkhoff方程相关联的矩阵Λ关键词：广义Birkhoff系统Birkhoff对称性守恒量矩阵迹 相似文献
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In this paper, the stability with respect to partial variables for theBirkhoff system is studied. By transplanting the results of the partialstability for general systems to the Birkhoff system and constructing asuitable Liapunov function, the partial stability of the system can beachieved. Finally, two examples are given to illustrate the application ofthe results. 相似文献
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研究广义Birkhoff系统的平衡稳定性问题.建立了自治广义Birkhoff系统的平衡方程;给出了自治广义Birkhoff系统的一次近似方程,利用Lyapunov一次近似理论,建立了系统平衡状态稳定性的判据;构建了Lyapunov函数,利用Lyapunov直接法,建立了自治广义Birkhoff系统平衡状态稳定性的判据.给出了若干算例以说明结果的应用. 相似文献
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广义Birkhoff系统的时间积分定理 总被引：1，自引：0，他引：1
研究了广义Birkhoff系统的时间积分定理.给出系统的时间积分等式,并由此等式导出类能量方程、类维里定理、一个积分变分原理和一个微分变分原理.关键词：广义Birkhoff系统时间积分定理类能量方程变分原理 相似文献
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场方法和最终乘子法是求解运动微分方程的基本方法.本文将这两种方法应用于广义Birkhoff系统,求出了场方法的基本偏微分方程和该方程的完全积分;根据Jacobi最终乘子定理求出了广义Birkhoff方程的解.并举例说明结果的应用. 相似文献
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In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results. 相似文献
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This paper presents a Poisson theory of the generalized Birkhoffequations, including the algebraic structure of the equations, thesufficient and necessary condition on the integral and theconditions under which a new integral can be deduced by a knownintegral as well as the form of the new integral. 相似文献
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In this paper, the stability of equilibrium state manifold for relativistic Birkhoffian systems in studied. The equilibrium state equations, the disturbance equations and their first approximation are presented. The criteria of stability for the equilibrium state manifold are obtained. The relationship between the stability of the equilibrium-state manifold of relativistic Birkhoffian systems and that of classical Birkhoffian systems is discussed. An example is given to illustrate the results. 相似文献
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C. Gruber 《Journal of statistical physics》1976,14(1):81-86
It is shown that there exists a phase transition associated with a singularity of the free energy for a model such that for all temperatures the equilibrium state is unique and thus stable with respect to boundary perturbations. It is also shown on this model that there exist phase transitions without symmetry breakdown, which can be related to a phase transition with symmetry breakdown on an equivalent model. 相似文献
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广义Birkhoff系统的积分不变量 总被引：2，自引：0，他引：2
研究广义Birkhoff系统的积分不变量.给出系统存在积分不变量的条件,在此条件下导出系统的线性积分不变量、通用积分不变量和二阶绝对积分不变量.举例说明结果的应用.关键词：广义Birkhoff方程线性积分不变量通用积分不变量二阶绝对积分不变量 相似文献
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Ricardo Almeida Ravi P. Agarwal Snezhana Hristova Donal O&#x;Regan 《Entropy (Basel, Switzerland)》2022,24(3)
A model of gene regulatory networks with generalized proportional Caputo fractional derivatives is set up, and stability properties are studied. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are discussed, and also, their application to fractional order systems and the advantage of quadratic functions are pointed out. The equilibrium of the generalized proportional Caputo fractional model and its generalized exponential stability are defined, and sufficient conditions for the generalized exponential stability and asymptotic stability of the equilibrium are obtained. As a special case, the stability of the equilibrium of the Caputo fractional model is discussed. Several examples are provided to illustrate our theoretical results and the influence of the type of fractional derivative on the stability behavior of the equilibrium. 相似文献