Citation: | ZHU Jianqu, JIN Weidong, GUO Feng. Stochastic Resonance of Fractional-Order System with Multiplicative Noise and Random Delay[J]. Journal of Southwest Jiaotong University, 2021, 56(2): 363-370. doi: 10.3969/j.issn.0258-2724.20191181 |
董小娟,晏爱君. 双稳态系统中随机共振和相干共振的相关性[J]. 物理学报,2013,62(7): 56-62.
DONG Xiaojuan, YAN Aijun. The relationship between stochastic resonance and coherence resonance in a bi-stable system[J]. Acta Physica Sinica, 2013, 62(7): 56-62.
|
焦尚彬,杨蓉,张青,等. α稳定噪声驱动的非对称双稳随机共振现象[J]. 物理学报,2015,64(2): 49-57.
JIAO Shangbin, YANG Rong, ZHANG Qing, et. al. Stochastic resonance of asymmetric bistable system with Alpha stable noise[J]. Acta Physica Sineca, 2015, 64(2): 49-57.
|
GUO Feng, ZHOU Yurong, JIANG Shiqi, et al. Stochastic resonance in a mono-stable system with multiplicative and additive noise[J]. Journal of Physics A: Mathematical and General, 2006, 39: 1386.1-1386.8. doi: 10.1088/0305-4470/39/45/002
|
LIU Yulei, LIANG Jun, JIAO Shangbin, et al. Stochastic resonance of a tri-stable system with α stable noise[J]. Chinese Journal of Physics, 2017, 55: 355-366. doi: 10.1016/j.cjph.2016.12.010
|
钟苏川,蔚涛,张路,等. 具有质量及频率涨落的欠阻尼线性谐振子的随机共振[J]. 物理学报,2105,64(2): 28-34.
ZHONG Suchuan, YU Tao, ZHANG Lu, et al. Stochastic resonance of an underdamped linear harmonic oscillator with fluctuating mass and fluctuating frequency[J]. Acta Physica Sineca, 2105, 64(2): 28-34.
|
FRANK T D, BEEK P J. Stationary solutions of linear stochastic delay differential equations:applications to biological systems[J]. Physical Review E, 2001, 64: 021917.1-021917.12.
|
MAJER N, SCHOLL E. Resonant control of stochastic spatiotemporal dynamics in a tunnel diode by multiple time-delayed feedback[J]. Physical Review E, 2009, 79: 011109.1-011109.8.
|
ZENG C H, SUN Y L, CHEN G X. The relaxation time of a bistable system with two different kinds of time delays[J]. Modern Physics Letters B, 2009, 23(18): 2281-2292.
|
GUO Feng, ZHOU Yurong, ZHANG Yu. Stochastic resonance in a time-delayed bistable system subject to multiplicative and additive noise[J]. Chinese Physics B, 2010, 19 (7): 90-94.
|
贺利芳,杨玉蕾,张天骐. 时延反馈EVG系统随机共振特性研究及轴承故障诊断[J]. 仪器仪表学报,2019,40(8): 47-57.
HE Lifang, YANG Yulei, ZHANG Tianqi. Stochastic resonance characteristic study and bearing fault diagnosis of time-delayed feedback EVG system[J]. Chinese Journal of Scientific Instrument, 2019, 40(8): 47-57.
|
SHI Peiming, XIA Haifeng, HAN Dongying, et al. Dynamical complexity and stochastic resonance in an asymmetry bistable system with time delay[J]. Chinese Journal of Physics., 2017, 55(1): 133-141. doi: 10.1016/j.cjph.2016.10.013
|
BAO H B, CAO J D. Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay[J]. Neural Networks, 2011, 24: 19-28. doi: 10.1016/j.neunet.2010.09.010
|
FINERTY J P. The population ecology of cycles in small mammals[M]. New Haven: Yale University Press, 1980.
|
FLOWEDEW J R. Mammls: their reproductive biology and population ecology[M]. London: Edward Arnold, 1987.
|
KILBAS A A, SARIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. New York: Elsevier, 2006.
|
高仕龙,钟苏川,韦鹏,等. 过阻尼分数阶Langeven方程及其随机共振[J]. 物理学报,2012,61(10): 32-37.
GAO Shilong, ZHONG Suchuan, WEI Peng, et al. Overdamped fractional Langevein equation and its stochastic resonance[J]. Acta Physica Sineca, 2012, 61(10): 32-37.
|
MÜLLER S, KÄSTNER M, BRUMMUND J, et al. On the numerical handling of fractional viscoelastic material models in a FE analysis[J]. Computing Mechanics, 2013, 51(6): 999-1012. doi: 10.1007/s00466-012-0783-x
|
公徐路,许鹏飞. 含时滞反馈与涨落质量的记忆阻尼系统的随机共振[J]. 力学学报,2018,50(4): 880-889. doi: 10.6052/0459-1879-18-051
GONG Xulu, XU Pengfei. Stochastic resoancne of a memorial-damped system with time delay feedback and fluctuating mass[J]. Chinses Journal of Theoretical and Applied Mechanics, 2018, 50(4): 880-889. doi: 10.6052/0459-1879-18-051
|
XU Yong, LI Yongge, LIU Di, et al. Responses of Duffing oscillator with fractional damping and random phase[J]. Nonlinear Dynamics, 2013, 74: 745-753. doi: 10.1007/s11071-013-1002-9
|
SHEN Yongjun, YANG Shaopu, XING Haijun, et al. Primary resonance of Duffing oscillator with two kinds of fractional-order derivatives[J]. International Journal of Non-Linear Mechanics, 2012, 47: 975-983. doi: 10.1016/j.ijnonlinmec.2012.06.012
|
LEUNG A Y T, GUO Zhongjin, YANG H X. Fractional derivative and time delay damper characteristics in Duffing-van der Pol oscillators[J]. Communicaton on Nonlinear Science and Numerical Simulation, 2013, 18: 2900-2915. doi: 10.1016/j.cnsns.2013.02.013
|
ZHU Jianqu, JIN Weidong, GUO Feng. Stochastic resonance for a linear oscillator with two kinds of fractional derivatives and random frequency[J]. Journal of Korean Physical Society, 2017, 70(8): 745-750. doi: 10.3938/jkps.70.745
|
ERKKI S, ROMI M, AIN A. Resonant behavior of a fractional oscillator with fluctuating frequency[J]. Physical Review E, 2010, 81(1): 011141.1-011141.11.
|
LIN Lifeng, CHEN Cong, WANG Huiqi. Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency[J]. Journal of Statistical Mechanics:Theory and Experement, 2016, 2: 023201.1-023201.21.
|
GUO Feng, ZHU Chengyin, CHENG Xiaofeng, et al. Stochastic resonance in a fractional harmonic oscillator subject to random mass and signal-modulated noise[J]. Physica A:Statistical Mechanics and Its Application, 2016, 459: 86-91. doi: 10.1016/j.physa.2016.04.011
|
DU Luchun, MEI Dongcheng. Effects of time delay on stochastic resonance of a periodically driven linear system with multiplicative and periodically modulated additive white noises[J]. Chinese Physics B, 2009, 18(3): 946-951. doi: 10.1088/1674-1056/18/3/018
|
GAO Shilong. Generalized stochastic resonance in a linear fractional system with a random delay[J]. Journal of Statistical Mechanics:Theory and Experiment, 2012: P12011.1-P12011.16.
|
VAN KAMPEN N G. Stochastic processes in physics and chemistry[M]. Amsterdam: [s.n.], 1992.
|
FULINSKI A. Non-Markovian noise[J]. Physical Review E, 1994, 50: 2668-2681. doi: 10.1103/PhysRevE.50.2668
|
GUILLOUZIC S, HEUREUX I L, LONGTIN A. Small delay approximation of stochastic delay differential equations[J]. Physical Review E, 1999, 59: 3970-3982. doi: 10.1103/PhysRevE.59.3970
|
SHAPIRO V E, LOGINOV V M. Formulae of differentiation and their use for solving stochastic equations[J]. Physica A, 1978, 91: 563-574. doi: 10.1016/0378-4371(78)90198-X
|
SELLERIO A L, MARI D, GREMAUD G. Fractional Brownian motion and anomalous diffusion in vibrated granular materials[J]. Journal of Statistical Mechanics:Theory and Experiment, 2012: P01002.1-P01002.18.
|