具有时间延迟的对称双稳系统迁移的对称性
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摘要
研究了一种具有时间延迟的、由加性白噪声与乘性白噪声驱动的对称双稳系统。通过时间延迟近似方法获取和对称双稳系统相应的福克-普朗克方程,给出福克-普朗克方程的稳态概率分布函数。当左势井向右势井迁移时,在噪声强度高于势垒高度的情况下,给出对称双稳系统的平均首通时间和对应的迁移率计算公式。当右势井向左势井迁移时,在噪声强度不超过势垒高度的情况下,通过最陡下降法计算具有时间延迟的对称双稳系统的平均首通时间和相应的迁移率。依据左势井向右势井迁移激活率公式和右势井向左势井迁移激活率公式获取迁移率与噪声比之间的关系。结果表明:时间延迟能够提高双稳系统的共振抑制,左势井到右势井的迁移与右势井到左势井的迁移是对称的,整个双稳系统也是对称的。
A kind of time delay is studied by the additive and multiplicative white noise and white noise driven asymmetric bistable system, obtained through approximation of time delay and asymmetric bistable system corresponding Fokker-Planck equation formula, given Fokker Planck equation for steady state probability distribution function of the formula. When left potential well potential well migration to the right,in the case of noise intensity is higher than the barrier height,average of asymmetric bistable system is given first time and the corresponding formula of mobility. When potential well potential well to the left right transfer,the noise intensity under the condition of no more than barrier height,by the steepest descent method to calculate the asymmetric bistable system with time delay of the first operating time and the corresponding average mobility. According to left potential well potential well to the right migration activation rate formula potential well potential well to the left and right migration activation rate formula to obtain the relationship between mobility and noise ratio,the result shows that time delay can improve the resonance of bistable system restrain,left potential well to the right of potential well migration potential well to the left and right potential well migration is symmetrical, the bistable system is symmetric.
A kind of time delay is studied by the additive and multiplicative white noise and white noise driven asymmetric bistable system, obtained through approximation of time delay and asymmetric bistable system corresponding Fokker-Planck equation formula, given Fokker Planck equation for steady state probability distribution function of the formula. When left potential well potential well migration to the right,in the case of noise intensity is higher than the barrier height,average of asymmetric bistable system is given first time and the corresponding formula of mobility. When potential well potential well to the left right transfer,the noise intensity under the condition of no more than barrier height,by the steepest descent method to calculate the asymmetric bistable system with time delay of the first operating time and the corresponding average mobility. According to left potential well potential well to the right migration activation rate formula potential well potential well to the left and right migration activation rate formula to obtain the relationship between mobility and noise ratio,the result shows that time delay can improve the resonance of bistable system restrain,left potential well to the right of potential well migration potential well to the left and right potential well migration is symmetrical, the bistable system is symmetric.
引文
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8 厉天威,罗兵,傅明利,等.550 k V交流滤波器断路器灭弧室电场计算.南方电网技术,2016;10(1):26—31Li Tianwei,Luo Bing,Fu Mingli,et al.Electric field calculation on arc-extinguishing chamber of 550 k V AC filter circuit breaker.Southern Power System Technology,2016;10(1):26—31
9 Syta A,Litak G,Friswell M I.Multiple solutions and corresponding power output of a nonlinear bistable piezoelectric energy harvester.The European Physical Journal B,2016;89(4):1—7
10 Simoyi R H.Pattern formation and symmetry-breaking bifurcations fueled by dissipation of chemical energy:a possible model for morphogenesis?Pure and Applied Chemistry,2014;71(6):1007—1017
11 王国威,程庆华,徐大海.关联噪声和周期信号驱动非对称双稳系统的稳态分析.量子电子学报,2014;31(1):86—93Wang Guowei,Cheng Qinghua,Xu Dahai.Steady-state analysis of an asymmetric bistable system driven by cross-correlated noises with periodic signal.Chinese Journal of Quantum Electronics,2014;31(1):86—93
12 孙中奎,鲁捧菊,徐伟,等.非对称双稳耦合网络系统的尺度随机共振研究.物理学报,2014;63(22):88—95Sun Zhongkui,Lu Pengju,Xu Wei,et al.Asymmetric coupled bistable stochastic resonance of the scale of the network system of research.Acta Physica Sinica,2014;63(22):88—95
13 夏玲玲,刘宜成,刘欣燚.永磁同步风电系统网侧变换器控制策略研究.计算机仿真,2014;31(11):113—116Xia Lingling,Liu Yicheng,Liu Xinyi.Study on grid side converter control strategy of permanent magnet synchronous wind power system.Computer Simulation,2014;31(11):113—116
14 Long F.Time-delay induced symmetry restoration and noise enhanced stability phenomena under correlated noises in an asymmetric bistable system.Indian Journal of Physics,2014;88(10):1111—1116
15 Wang G W,Cheng Q H,Da-Hai X U.Steady-state analysis of an asymmetric bistable system driven by cross-correlated noises with periodic signal.Chinese Journal of Quantum Electronics,2014;31(1):86—93
16 杨文荣,薛力升,朱佳斌.基于LLC谐振变换器的X光机高压电源设计与仿真.计算机测量与控制,2016;24(2):155—157Yang Wenrong,Xue Lisheng,Zhu Jiabin.Design and simulation of high voltage power supply for X-Ray machine based on LLC resonant converter.Computer Measurement&Control,2016;24(2):155—157
17樊艺.拟线性双曲系统复函数自伴扰动稳定性正解.科技通报,2015;31(8):12—14Fan Yi.Self adjoint perturbation stability positive solutions of quasilinear hyperbolic systems complex function.Bulletin of Science and Technology,2015;31(8):12—14
18 贺利芳,崔莹莹,张天骐.基于非线性耦合双稳系统的微弱信号检测研究.科学技术与工程,2016;16(2):72—77He Lifang,Cui Yingying,Zhang Tianqi.Research on weak signal detection based on nonlinear coupled bistable systems.Science Technology and Engineering,2016;16(2):72—77
19 徐鸿鹏,尹社会,张勇.一个超混沌类Lorenz系统的非线性动力学行为及计算机仿真.电子设计工程,2016;24(10):38—41Xu Hongpeng,Yin Shehui,Zhang Yong.Nonlinear dynamic behavior of a Lorenz-like hyperchaotic system and its computer simulation.Electronic Design Engineering,2016;24(10):38—41
20 Shi P,Li Q,Han D.Stochastic resonance in a new asymmetric bistable system driven by unrelated multiplicative and additive noise.Chinese Journal of Physics,2016;54(4):526—532
2 赵燕.非高斯噪声激励下双稳系统的平均首次穿越时间.西安文理学院学报:自然科学版,2016;19(5):21—25Zhao Yan.The mean first passage time for a bi-stable system driven by non-gaussian noise.Journal of Xi’an University(Natural Science Edition),2016;19(5):21—25
3 张瑞芳,程庆华,徐大海,等.周期力调制下色关联色噪声驱动光学双稳系统的光强相对涨落.量子电子学报,2015;32(1):96 —100Zhang Ruifang,Cheng Qinghua,Xu Dahai,et al.Fluctuation of optical bistable system driven by color-correlated colored noise with periodic force modulation.Chinese Journal of Quantum Electronics,2015;32(1):96—100
4 Li C,Jia Z L,Mei D C.Effects of correlation time between noises on the noise enhanced stability phenomenon in an asymmetric bistable system.Frontiers of Physics,2015;10(1):95—101
5 Palacios A,In V,Longhini P.Symmetry-breaking as a paradigm to design highly-sensitive sensor systems.Symmetry,2015;7(2):1122—1150
6 刘璐,谷开慧,刑淑芝,等.基于耦合映像格子模型的电光双稳系统的时空混沌控制.吉林化工学院学报,2015;32(8):53—55Liu Lu,Gu Kaihui,Xing Shuzhi,et al.Spatiotemporal chaos control in coupled electrical-optical bistable map lattice system.Journal of Jilin Institute of Chemical Technology,2015;32(8):53—55
7 陈威霖,及春宁,徐万海.并列双圆柱流致振动的不对称振动和对称性迟滞研究.力学学报,2015;47(5):731—739Chen Weilin,Ji Chunning,Xu Wanhai.Numerical investigation on the asymmetric vibration and symmetry hysteresis of flow-induced vibration of two side-by-side cylinders.Chinese Journal of Theoretical and Applied Mechanics,2015;47(5):731—739
8 厉天威,罗兵,傅明利,等.550 k V交流滤波器断路器灭弧室电场计算.南方电网技术,2016;10(1):26—31Li Tianwei,Luo Bing,Fu Mingli,et al.Electric field calculation on arc-extinguishing chamber of 550 k V AC filter circuit breaker.Southern Power System Technology,2016;10(1):26—31
9 Syta A,Litak G,Friswell M I.Multiple solutions and corresponding power output of a nonlinear bistable piezoelectric energy harvester.The European Physical Journal B,2016;89(4):1—7
10 Simoyi R H.Pattern formation and symmetry-breaking bifurcations fueled by dissipation of chemical energy:a possible model for morphogenesis?Pure and Applied Chemistry,2014;71(6):1007—1017
11 王国威,程庆华,徐大海.关联噪声和周期信号驱动非对称双稳系统的稳态分析.量子电子学报,2014;31(1):86—93Wang Guowei,Cheng Qinghua,Xu Dahai.Steady-state analysis of an asymmetric bistable system driven by cross-correlated noises with periodic signal.Chinese Journal of Quantum Electronics,2014;31(1):86—93
12 孙中奎,鲁捧菊,徐伟,等.非对称双稳耦合网络系统的尺度随机共振研究.物理学报,2014;63(22):88—95Sun Zhongkui,Lu Pengju,Xu Wei,et al.Asymmetric coupled bistable stochastic resonance of the scale of the network system of research.Acta Physica Sinica,2014;63(22):88—95
13 夏玲玲,刘宜成,刘欣燚.永磁同步风电系统网侧变换器控制策略研究.计算机仿真,2014;31(11):113—116Xia Lingling,Liu Yicheng,Liu Xinyi.Study on grid side converter control strategy of permanent magnet synchronous wind power system.Computer Simulation,2014;31(11):113—116
14 Long F.Time-delay induced symmetry restoration and noise enhanced stability phenomena under correlated noises in an asymmetric bistable system.Indian Journal of Physics,2014;88(10):1111—1116
15 Wang G W,Cheng Q H,Da-Hai X U.Steady-state analysis of an asymmetric bistable system driven by cross-correlated noises with periodic signal.Chinese Journal of Quantum Electronics,2014;31(1):86—93
16 杨文荣,薛力升,朱佳斌.基于LLC谐振变换器的X光机高压电源设计与仿真.计算机测量与控制,2016;24(2):155—157Yang Wenrong,Xue Lisheng,Zhu Jiabin.Design and simulation of high voltage power supply for X-Ray machine based on LLC resonant converter.Computer Measurement&Control,2016;24(2):155—157
17樊艺.拟线性双曲系统复函数自伴扰动稳定性正解.科技通报,2015;31(8):12—14Fan Yi.Self adjoint perturbation stability positive solutions of quasilinear hyperbolic systems complex function.Bulletin of Science and Technology,2015;31(8):12—14
18 贺利芳,崔莹莹,张天骐.基于非线性耦合双稳系统的微弱信号检测研究.科学技术与工程,2016;16(2):72—77He Lifang,Cui Yingying,Zhang Tianqi.Research on weak signal detection based on nonlinear coupled bistable systems.Science Technology and Engineering,2016;16(2):72—77
19 徐鸿鹏,尹社会,张勇.一个超混沌类Lorenz系统的非线性动力学行为及计算机仿真.电子设计工程,2016;24(10):38—41Xu Hongpeng,Yin Shehui,Zhang Yong.Nonlinear dynamic behavior of a Lorenz-like hyperchaotic system and its computer simulation.Electronic Design Engineering,2016;24(10):38—41
20 Shi P,Li Q,Han D.Stochastic resonance in a new asymmetric bistable system driven by unrelated multiplicative and additive noise.Chinese Journal of Physics,2016;54(4):526—532