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It is improper to use frequency domain signal-to-noise ratio as a measure to judge whether stochastic resonance happens with chirp signal which is common in engineering. As a result, there is little literature on this subject. Using the energy aggregation in an optimal fractional Fourier transform domain of chirp signal, in this paper we propose a new signal-to-noise ratio defined in an optimal fractional domain to study the stochastic resonance of over-damped bistable system driven by chirp signal and Gaussian white noise. A new phenomenon is found, that is, the stochastic resonance phenomenon weakens gradually as the frequency of chirp signal increases. And it is reasonably explained in this paper. The consistency of simulation results with theoretical analysis verifies the effectiveness of the method proposed in this paper.
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Keywords:
- chirp signal /
- fractional Fourier transform /
- stochastic resonance
[1] Benzi R, Suter A, Vulpana A 1981 Physica A 14 L453
[2] Benzi R, Parisi G, Suter A, Vulpana A 1982 Tellus 34 11
[3] Gitterman M 2003 Phys. Rev. E 67 057103
[4] Jia Y, Yu S N, Li J R 2000 Phys. Rev. E 62 1869
[5] Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[6] Luo X, Zhu S 2003 Phys. Rev. E 67 021104
[7] Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 3321
[8] Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575
[9] McNamara B, Wiesenfel K 1989 Phys. Rev. A 39 4854
[10] Tao R, Qin L, Wang Y 2004 Theory and Applications of the Fractional Fourier Transform (1st Ed.) (Beijing:Tsinghua University Press) p111 (in Chinese) [陶然, 齐林, 王越 2004 分数阶Fourier变换的原理与应用(第一版) (北京:清华大学出版社) 第111页]
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[1] Benzi R, Suter A, Vulpana A 1981 Physica A 14 L453
[2] Benzi R, Parisi G, Suter A, Vulpana A 1982 Tellus 34 11
[3] Gitterman M 2003 Phys. Rev. E 67 057103
[4] Jia Y, Yu S N, Li J R 2000 Phys. Rev. E 62 1869
[5] Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[6] Luo X, Zhu S 2003 Phys. Rev. E 67 021104
[7] Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 3321
[8] Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575
[9] McNamara B, Wiesenfel K 1989 Phys. Rev. A 39 4854
[10] Tao R, Qin L, Wang Y 2004 Theory and Applications of the Fractional Fourier Transform (1st Ed.) (Beijing:Tsinghua University Press) p111 (in Chinese) [陶然, 齐林, 王越 2004 分数阶Fourier变换的原理与应用(第一版) (北京:清华大学出版社) 第111页]
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