Stochastic resonance for a fractional linear oscillator with two-kinds of fractional-order derivatives subject to multiplicative and signal-modulated noise

• Published in: Chinese journal of physics (Taipei) Vol. 55; no. 3; pp. 853 - 861
• Main Authors: Zhu, Jianqu, Jin, Weidong, Guo, Feng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2017
• Subjects: Fractional linear oscillator; Multiplicative noise; Random frequency; Stochastic resonance; Random frequency; Fractional linear oscillator; Multiplicative noise; Stochastic resonance
• ISSN: 0577-9073
• DOI: 10.1016/j.cjph.2016.11.014

•A fractional linear oscillator with two-kinds of fractional-order derivatives is investigated.•The output-gain is a non-monotonic function of the exponents of the fractional-order derivatives.•The effect of the two exponents on the OAG is different.•The output-gain varies non-monotonically with the driving frequency.•The output-gain behaves non-monotonically with the friction coefficients. The stochastic resonance phenomenon for a fractional linear oscillator with two-kinds of fractional-order derivatives driven by multiplicative noise and signal-modulated noise is investigated. Based on linear system theory, applying the characteristics of the Gamma function and the definition of the fractional-order derivative, the output-amplitude-gain (OAG) for the oscillator is derived. The analysis results show that the OAG is a non-monotonic function of the exponents of the fractional-order derivatives, the effect of the two exponents on the OAG is different. The OAG varies non-monotonically with a variation of the system driving frequency. The OAG behaves non-monotonically with an increase of the two friction coefficients of the fractional oscillator. The nonlinear dependence of the system frequency and the correlation rate of the multiplicative noise are analyzed.