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Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators

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  • Gandhimathi, V.M.
  • Murali, K.
  • Rajasekar, S.

Abstract

We study the stochastic resonance phenomenon in the overdamped two coupled anharmonic oscillators with Gaussian noise and driven by different external periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth, (iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidal forces. The external periodic forces and Gaussian noise term are added to one of the two state variables of the system. The effect of each force is studied separately. In the absence of noise term, when the amplitude f of the applied periodic force is varied cross-well motion is realized above a critical value (fc) of f. This is found for all the forces except the modulus of sine and rectified sinusoidal forces. For fixed values of angular frequency ω of the periodic forces, fc is minimum for square wave and maximum for asymmetric saw-tooth wave. fc is found to scale as Ae0.75ω+B where A and B are constants. Stochastic resonance is observed in the presence of noise and periodic forces. The effect of different forces is compared. The stochastic resonance behaviour is quantized using power spectrum, signal-to-noise ratio, mean residence time and distribution of normalized residence times. The logarithmic plot of mean residence time τMR against 1/(D−Dc) where D is the intensity of the noise and Dc is the value of D at which cross-well motion is initiated shows a sharp knee-like structure for all the forces. Signal-to-noise ratio is found to be maximum at the noise intensity D=Dmax at which mean residence time is half of the period of the driving force for the forces such as sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. With modulus of sine wave and rectified sine wave, the SNR peaks at a value of D for which sum of τMR in two wells of the potential of the system is half of the period of the driving force. For the chosen values of f and ω, signal-to-noise ratio is found to be maximum for square wave while it is minimum for modulus of sine and rectified sinusoidal waves. The values of Dc at which cross-well behaviour is initiated and Dmax are found to depend on the shape of the periodic forces.

Suggested Citation

  • Gandhimathi, V.M. & Murali, K. & Rajasekar, S., 2006. "Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1034-1047.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:5:p:1034-1047
    DOI: 10.1016/j.chaos.2005.09.046
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    References listed on IDEAS

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    1. Sinha, Sitabhra, 1999. "Noise-free stochastic resonance in simple chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 204-214.
    2. Valenti, D. & Fiasconaro, A. & Spagnolo, B., 2004. "Stochastic resonance and noise delayed extinction in a model of two competing species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 477-486.
    3. Gandhimathi, V.M. & Murali, K. & Rajasekar, S., 2005. "Stochastic resonance in overdamped two coupled anharmonic oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 99-116.
    4. Carusela, M.F. & Codnia, J. & Romanelli, L., 2003. "Stochastic resonance: numerical and experimental devices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 415-420.
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    Cited by:

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    2. Srinivasan, K. & Thamilmaran, K. & Venkatesan, A., 2009. "Effect of nonsinusoidal periodic forces in Duffing oscillator: Numerical and analog simulation studies," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 319-330.
    3. Cang, Shijian & Zhao, Gehang & Wang, Zenghui & Chen, Zengqiang, 2022. "Global structures of clew-shaped conservative chaotic flows in a class of 3D one-thermostat systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Wei, Mengke & Han, Xiujing, 2024. "Fast–slow dynamics related to sharp transition behaviors in the Rayleigh oscillator with two slow square wave excitations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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