| Lyapunov function as potential function： A dynamical equivalence |
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| 引用本文： | 袁若石,马易安,苑波,敖平.Lyapunov function as potential function： A dynamical equivalence[J].中国物理 B,2014,23(1):10505-010505. |
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| 作者姓名： | 袁若石 马易安 苑波 敖平 |
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| 作者单位： | a School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;b Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China;c Department of Applied Mathematics, University of Washington, Seattle 98195, USA;d Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;e Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China |
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| 基金项目： | Project supported by the National Basic Research Program of China(Grant No.2010CB529200);the National Natural Science Foundation of China(Grant Nos.61073087 and 91029738) |
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| 摘 要： | For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization: a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.
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| 关 键 词： | Lyapunov function potential function stochastic process generalized Einstein relation |
| 收稿时间： | 2013-03-20 |
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