Oscillator Subject to Periodic and Random Forces

ABSTRACT

We illustrate the influence of an external periodic force and noise on a physical system by the example of an oscillator. These two forces seem to be the reverse of each other, since the latter leads to disorder while the former works in an orderly fashion. Nevertheless, it is shown that they may influence a system in a similar way, sometime even substituting for one another. These examples serve to illustrate one of the main achievements of twentieth-century physics, which has established that deterministic and random phenomena complement rather than contradict each other.

KEYWORDS

Stochastic Oscillator; Periodic Force; Stochastic and Vibrational Resonances; Birth-Death Process

Stochastic Oscillator; Periodic Force; Stochastic and Vibrational Resonances; Birth-Death Process

Cite this paper

M. Gitterman, "Oscillator Subject to Periodic and Random Forces,"*Journal of Modern Physics*, Vol. 4 No. 1, 2013, pp. 94-98. doi: 10.4236/jmp.2013.41015.

M. Gitterman, "Oscillator Subject to Periodic and Random Forces,"

References

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[17] R. N. Mantegna and R. Spagnolo, “Noise Enhanced Stability in an Unstable System,” Physical Review Letters, Vol. 76, No. 4, 1996, pp. 563-566. doi:10.1103/PhysRevLett.76.563

[18] L. Landau and E. Lifshitz, “Mechanics,” Mechanics, Pergamon, 1976.

[19] M. Gitterman, “Stabilization of Metastable States,” Physical Review E, Vol. 65, No. 3, 2002, Article ID: 031103. doi:10.1103/PhysRevE.65.031103

[20] M. Gitterman, “Mean-Square Displacement of a Stochastic Oscillator: Linear vs. Quadratic Noise,” Physica A, Vol. 391, No. 11, 2012, pp. 3033-3048. doi:10.1016/j.physa.2012.01.021

[21] P. S. Landa and P. V. E. McClintock, “Vibrational Resonance,” Journal of Physics A, Vol. 33, No. 45, 2000, pp. L433-L438.

[22] Y. M. Kang, J.-X. Xu and Y. Xie, “Observing Stochastic Resonance in an Underdamped Bistable Duffing Oscillator by the Method of Moments,” Physical Review E, Vol. 68, No. 3, 2003, Article ID: 036123. doi:10.1103/PhysRevE.68.036123

[1] R. Dean Astumian and F. Moss, “Overview: The Constructive Role of Noise in Fluctuations of Driven Transport and Stochastic Resonance,” Chaos, Vol. 8, No. 5, 1998, pp. 533-539. doi:10.1063/1.166334

[2] W. Horsthemke and R. Lefever, “Noise-Induced Transitions,” Springer, Berlin, 1084.

[3] P. Hanggi and R. Bartussek, “Lecture Notes in Physics,” Springer, Berlin, 1996.

[4] J. M. R. Parrondo, C. Van den Broeck and F. de la Rubia, “Noise-Induced Spatial Patterns,” Physica A, Vol. 224, No. 1-2, 1996, pp. 153-161. doi:10.1016/0378-4371(95)00350-9

[5] P. Yung and P. Talkner, “Suppression of Higher Harmonics at Noise Induced Resonances,” Physical Review E, Vol. 51, No. 3, 1995, pp. 2640-2643. doi:10.1103/PhysRevE.51.2640

[6] I. Dayan, M. Gitterman and G. H. Weiss, “Stochastic Resonance in Transient Dynamics,” Physical Review A, Vol. 46, No. 2, 1992, pp. 757-761. doi:10.1103/PhysRevA.46.757

[7] S. L. Ginzburg and M. A. Pustovoit, “Noise-Induced Hypersensitivity to Small Time-Dependent Signals,” Physical Review Letters, Vol. 80, No. 22, pp. 4840-4842. doi:10.1103/PhysRevLett.80.4840

[8] C. R. Doering and J. C. Gadoua, “Resonant Activation over a Fluctuating Barrier,” Physical Review Letters, Vol. 69, No. 16, 1992, pp. 2318-2321. doi:10.1103/PhysRevLett.69.2318

[9] F. Marchesoni, “Conceptual Design of a Molecular Shuttle,” Physical Letters A, Vol. 237, No. 3, 1998, pp. 126- 130.

[10] D. W. Brown, L. J. Bernstein and K. Lindenberg, “Resonant Activation over a Fluctuating Barrier,” Physical Review E, Vol. 54, No. 4, 1996, pp. 3352-3360. doi:10.1103/PhysRevE.54.3352

[11] G. Nicolis and I. Prigogine, “Self-Organization in Non-Equilibrium Systems,” Wiley, New York, 1977.

[12] J. E. Fletcher, S. Havlin and G. H. Weiss, “First Passage Time Problems in Time-Dependent Fields,” Journal of Statistical Physics, Vol. 51, No. 1-2, 1988, pp. 215-232. doi:10.1007/BF01015328

[13] P. Reimann and P. Hanggi, “Lecture Notes in Physics,” Springer, Berlin, 1997.

[14] C. Zhou and C.-H. Lai, “Robustness of Supersensitivity to Small Signals in Nonlinear Dynamical Systems,” Physical Review E, Vol. 59, No. 6, 1999, pp. R6243-R6246. doi:10.1103/PhysRevE.59.R6243

[15] P. Yung and E. Marchesoni, “Energetics of Stochastic Resonance,” Chaos, Vol. 21, No. 4, 2011, Article ID: 046516.

[16] M. Gitterman, “Order and Chaos: Are They Contradicting or Complimentary?” European Journal of Physics, Vol. 23, No. 2, 2002, pp. 119-122. doi:10.1088/0143-0807/23/2/304

[17] R. N. Mantegna and R. Spagnolo, “Noise Enhanced Stability in an Unstable System,” Physical Review Letters, Vol. 76, No. 4, 1996, pp. 563-566. doi:10.1103/PhysRevLett.76.563

[18] L. Landau and E. Lifshitz, “Mechanics,” Mechanics, Pergamon, 1976.

[19] M. Gitterman, “Stabilization of Metastable States,” Physical Review E, Vol. 65, No. 3, 2002, Article ID: 031103. doi:10.1103/PhysRevE.65.031103

[20] M. Gitterman, “Mean-Square Displacement of a Stochastic Oscillator: Linear vs. Quadratic Noise,” Physica A, Vol. 391, No. 11, 2012, pp. 3033-3048. doi:10.1016/j.physa.2012.01.021

[21] P. S. Landa and P. V. E. McClintock, “Vibrational Resonance,” Journal of Physics A, Vol. 33, No. 45, 2000, pp. L433-L438.

[22] Y. M. Kang, J.-X. Xu and Y. Xie, “Observing Stochastic Resonance in an Underdamped Bistable Duffing Oscillator by the Method of Moments,” Physical Review E, Vol. 68, No. 3, 2003, Article ID: 036123. doi:10.1103/PhysRevE.68.036123