Potential in stochastic differential equations: novel construction
Potential in stochastic differential equations: novel construction
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DOI：
10.1088/0305-4470/37/3/l01
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发表时间：
2004-01-23
期刊：
影响因子：
--
通讯作者：
Ao, P
中科院分区：
文献类型：
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作者：
Ao, P
复杂网络中存在一系列突现现象，如鲁棒性、自适应性、多重平衡、滞后、振荡和反馈等。这些非平衡行为通常可以用一组随机微分方程来描述。一个持续存在的重要问题是势函数的存在性。在这里，我们证明了一个动态结构内置于随机微分方程允许我们构造这样一个全局优化的势函数。我们提出了一个明确的施工程序，以获得电位和相关量。在这个过程中，不需要参考福克-普朗克方程。势的可用性表明，强大的统计力学工具可以用于非平衡状态。
There is a whole range of emergent phenomena in a complex network such as robustness, adaptiveness, multiple-equilibrium, hysteresis, oscillation and feedback. Those non-equilibrium behaviours can often be described by a set of stochastic differential equations. One persistent important question is the existence of a potential function. Here we demonstrate that a dynamical structure built into stochastic differential equation allows us to construct such a global optimization potential function. We present an explicit construction procedure to obtain the potential and relevant quantities. In the procedure no reference to the Fokker-Planck equation is needed. The availability of the potential suggests that powerful statistical mechanics tools can be used in nonequilibrium situations.