吴志强¹, 王耀光¹, 张祥云¹, 王喆²
AuthorsHTML:吴志强¹, 王耀光¹, 张祥云¹, 王喆²
AuthorsListE:Wu Zhiqiang¹, Wang Yaoguang¹, Zhang Xiangyun¹, Wang Zhe²
AuthorsHTMLE:Wu Zhiqiang¹, Wang Yaoguang¹, Zhang Xiangyun¹, Wang Zhe²
Unit:1. 天津大学机械工程学院，天津 300072；2. 天津理工大学理学院，天津 300384
Unit_EngLish:1. School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
2．School of Science, Tianjin University of Technology, Tianjin 300384, China
Abstract_Chinese:非线性系统的随机行为与其确定性行为有密切联系, 双稳态系统与三稳态系统的确定性行为有本质区别, 其随机P分岔有明显区别．针对确定性分岔定性相同的系统, 开展了广义van der Pol方程确定性分岔及随机P分岔现象的理论与实验研究．结果表明：确定性分岔相同的系统, 其随机P分岔行为不一定相同; 确定性情况下, 系统中存在三稳态现象; 在随机激励情况下, 稳定系数、噪声强度都会导致随机P分岔产生; 稳定系数不变情况下, 噪声强度变化能最多导致4次随机P分岔现象．
Abstract_English:The stochastic behavior of a nonlinear system is closely related to its deterministic behavior. The deterministic behavior of bistable system and tri-stable system is essentially different from each other，and the stochastic P bifurcation is obviously different. The theoretical and experimental researches on the deterministic bifurcation and stochastic P bifurcation of the generalized van der Pol equation are carried out for the system with the qualitatively same deterministic bifurcation. The results show that the stochastic P bifurcation behavior of the system with the same deterministic bifurcation is not necessarily the same. Under the deterministic condition，tri-stable phenomena exist in the system. In the case of stochastic excitation，stability coefficient and noise intensity can lead to stochastic P bifurcation. When stability coefficient is constant，the variation of noise intensity can lead to four stochastic P bifurcation phenomena at most.
Keyword_Chinese:广义van der Pol方程; 确定性分岔; 随机P分岔; 稳定系数; 噪声强度
Keywords_English:generalized van der Pol equation; deterministic bifurcation; stochastic P-bifurcation; stability coefficient; noise intensity

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