### Abstract

We study the influence of the shapes of three different external periodic forces on the stochastic resonance phenomenon in multiple potential well systems with Gaussian noise. We consider as external periodic forces the sine wave, the modulus of sine wave and the rectified sine wave. The systems of our interest are two coupled overdamped anharmonic oscillators and the Duffing oscillator. For fixed values of the parameters, when the intensity D of the external noise is varied, the systems with these periodic forces separately are found to exhibit stochastic resonance. Certain similarities and differences are found in the characteristics of these statistical measures such as signal-to-noise ratio (SNR), response amplitude (Q), time series plot, mean residence time tau(MR) in the potential wells and the distribution P of the normalized residence time for these different forces. Especially, the time series plot at the maximum SNR shows an almost periodic switching between the potential wells for the sine force which is not observed for the other two forces. In the noise-induced intermittent dynamics, tau(MR) is the same in different wells for the sine force, whereas it is different in different wells for the other two forces for each value of the noise intensity D. Further, variation of tau(MR) with D, the value of tau(MR) at the resonance and the distribution P show different features for the different types of forces. We present a detailed comparative study and explanation for the similarities and differences observed in the stochastic resonance dynamics.

Original language | English |
---|---|

Pages (from-to) | 2073-2088 |

Number of pages | 16 |

Journal | International Journal of Bifurcation and Chaos |

Volume | 18 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2008 |

### Keywords

- Two coupled overdamped anharmonic oscillators
- Duffing oscillator
- the sine wave
- the modulus of the sine wave
- the rectified sine wave
- signal-to-noise ratio
- mean residence time
- coupled anharmonic-oscillators
- vibrational resonance
- excitable systems
- chaos
- driven
- pulses

### Cite this

*International Journal of Bifurcation and Chaos*,

*18*(7), 2073-2088. https://doi.org/10.1142/S0218127408021579

**Effects of the Shape of Periodic Forces on Stochastic Resonance.** / Gandhimathi, V. M.; Rajasekar, S.; Kurths, J.

Research output: Contribution to journal › Article

*International Journal of Bifurcation and Chaos*, vol. 18, no. 7, pp. 2073-2088. https://doi.org/10.1142/S0218127408021579

}

TY - JOUR

T1 - Effects of the Shape of Periodic Forces on Stochastic Resonance

AU - Gandhimathi, V. M.

AU - Rajasekar, S.

AU - Kurths, J.

PY - 2008/7

Y1 - 2008/7

N2 - We study the influence of the shapes of three different external periodic forces on the stochastic resonance phenomenon in multiple potential well systems with Gaussian noise. We consider as external periodic forces the sine wave, the modulus of sine wave and the rectified sine wave. The systems of our interest are two coupled overdamped anharmonic oscillators and the Duffing oscillator. For fixed values of the parameters, when the intensity D of the external noise is varied, the systems with these periodic forces separately are found to exhibit stochastic resonance. Certain similarities and differences are found in the characteristics of these statistical measures such as signal-to-noise ratio (SNR), response amplitude (Q), time series plot, mean residence time tau(MR) in the potential wells and the distribution P of the normalized residence time for these different forces. Especially, the time series plot at the maximum SNR shows an almost periodic switching between the potential wells for the sine force which is not observed for the other two forces. In the noise-induced intermittent dynamics, tau(MR) is the same in different wells for the sine force, whereas it is different in different wells for the other two forces for each value of the noise intensity D. Further, variation of tau(MR) with D, the value of tau(MR) at the resonance and the distribution P show different features for the different types of forces. We present a detailed comparative study and explanation for the similarities and differences observed in the stochastic resonance dynamics.

AB - We study the influence of the shapes of three different external periodic forces on the stochastic resonance phenomenon in multiple potential well systems with Gaussian noise. We consider as external periodic forces the sine wave, the modulus of sine wave and the rectified sine wave. The systems of our interest are two coupled overdamped anharmonic oscillators and the Duffing oscillator. For fixed values of the parameters, when the intensity D of the external noise is varied, the systems with these periodic forces separately are found to exhibit stochastic resonance. Certain similarities and differences are found in the characteristics of these statistical measures such as signal-to-noise ratio (SNR), response amplitude (Q), time series plot, mean residence time tau(MR) in the potential wells and the distribution P of the normalized residence time for these different forces. Especially, the time series plot at the maximum SNR shows an almost periodic switching between the potential wells for the sine force which is not observed for the other two forces. In the noise-induced intermittent dynamics, tau(MR) is the same in different wells for the sine force, whereas it is different in different wells for the other two forces for each value of the noise intensity D. Further, variation of tau(MR) with D, the value of tau(MR) at the resonance and the distribution P show different features for the different types of forces. We present a detailed comparative study and explanation for the similarities and differences observed in the stochastic resonance dynamics.

KW - Two coupled overdamped anharmonic oscillators

KW - Duffing oscillator

KW - the sine wave

KW - the modulus of the sine wave

KW - the rectified sine wave

KW - signal-to-noise ratio

KW - mean residence time

KW - coupled anharmonic-oscillators

KW - vibrational resonance

KW - excitable systems

KW - chaos

KW - driven

KW - pulses

U2 - 10.1142/S0218127408021579

DO - 10.1142/S0218127408021579

M3 - Article

VL - 18

SP - 2073

EP - 2088

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

SN - 0218-1274

IS - 7

ER -