Share This Article:

Nature’s autonomous oscillators

Full-Text HTML XML Download Download as PDF (Size:1947KB) PP. 233-244
DOI: 10.4236/ns.2012.44034    4,512 Downloads   7,765 Views   Citations


Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature’s observed autonomous oscillators, examples are the quasi-biennial oscillation of the atmosphere and the 22- year solar oscillation [1]. Numerical models simulate the oscillations, and we discuss the nonlinearities that are involved. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity. The human heart also functions autonomously, and physiological arguments support the picture that the heart is a nonlinear oscillator.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Mayr, H. , Yee, J. , Mayr, M. and Schnetzler, R. (2012) Nature’s autonomous oscillators. Natural Science, 4, 233-244. doi: 10.4236/ns.2012.44034.


[1] Mayr, H.G., and Schatten, K.H. (2012) Nonlinear oscillators in space physics. Journal of Atmospheric and Solar- Terrestrial Physics, 74, 44-55. doi:10.1016/j.jastp.2011.09.008.
[2] Baldwin, M.P., Gray, L.J., Dunkerton, T.J., et al. (2001) The quasi-biennial oscillation. Review of Geophysics, 39, 179-229. doi:10.1029/1999RG000073.
[3] Lindzen, R.S. and Holton, J.R. (1968) A theory of the quasi-biennial oscillation. Journal of Atmospheric Science, 25, 1095-1107. doi:10.1175/1520-0469(1968)025<1095:ATOTQB>2.0.CO;2
[4] Mengel, J.G., Mayr, H.G., Chan, K.L., Hines, C.O., Reddy, C.A., Arnold, N.F. and Porter, H.S. (1995) Equatorial oscillations in the middle atmosphere generated by small scale gravity waves. Geophysics Research Letters, 22, 3027-3030. doi10.1029/95GL03059
[5] Dunkerton, T.J. (1997) The role of the gravity waves in the quasi-biennial oscillation. Journal of Geophysical Research, 102, 26053-26076. doi:10.1029/96JD02999.
[6] Holton, J.R. and Lindzen, R.S. (1972) An updated theory for the quasi-biennial cycle of the tropical stratosphere. Journal of Atmospheric Science, 29, 1076-1080. doi:10.1175/1520-0469(1972)029<1076:AUTFTQ>2.0.CO;2
[7] Mayr, H.G., Mengel, J.G. and Chan, K.L. (1998) Equatorial oscillations maintained by gravity waves as described with the Doppler Spread Parameterization: I. Numerical experiments. Journal of Atmospheric and Solar-Terres- trial Physics, 60, 181-199. doi:10.1016/S1364-6826(97)00122-3.
[8] Mayr, H.G., Mengel, J.G., Hines, C.O, Chan, C.L., Arnold, N.F., Reddy, C.A. and Porter, H.S. (1997) The gravity wave Doppler spread theory applied in a numerical spectral model of the middle atmosphere 1. Model and global scale variations. Journal of Geophysical Research, 102, 26077-26091. doi:10.1029/96JD03213.
[9] Hines, C.O. (1997) Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere. Part 1: Basic formulation. Journal of Atmospheric and Solar-Terrestrial Physics, 59, 371-386.
[10] Hines, C.O. (1997) Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere. Part 2: Broad and quasi monochromatic spectra, and implementation. Journal of Atmospheric and Solar- Terrestrial Physics, 59, 387-400.
[11] Mayr, H.G., Mengel, J.G., Reddy, C.A., Chan, K.L. and Porter, H.S. (1999) The role of gravity waves in maintaining the QBO and SAO at equatorial latitudes. Ad- vance in Space Research, 24, 1531-1540.
[12] Eckermann, S.D. and Vincent, R.A. (1994) First observations of intra-seasonal oscillations in the equatorial mesosphere and lower thermosphere. Geophysics Research Letters, 21, 265-268.
[13] Lieberman, R.S. (1998) Intraseasonal variability of high-resolution Doppler imager winds in the equatorial mesosphere and lower thermosphere. Journal of Geophysical Research, 103, 11221-11228. doi:10.1029/98JD00532.
[14] Huang, F.T. and Reber, C.A. (2003) Seasonal behavior of the semidiurnal and diurnal tides, and mean flows at 95 km, based on measurements from the High Resolution Doppler Imager (HRDI) on the Upper Atmosphere Research Satellite (UARS). Journal of Geophysical Research, 108, 4360-4376. doi:10.1029/2002JD003189.
[15] Mayr, H.G, Mengel, J.G., Drob, D.P., Porter, H.S. and Chan, K.L. (2003) Intraseasonal oscillations in the middle atmosphere forced by gravity waves. Journal of Atmospheric and Solar-Terrestrial Physics, 65, 1187-1203. doi:10.1016/j.jastp.2003.07.008.
[16] Schatten, K. (2005) Fair space weather for solar cycle 24. Geophysics Research Letters, 32, L21106-L21110. doi:10.1029/2005GL024363.
[17] Dikpati, M. and Charbonneau, P. (1999) A Babcock- Leighton flux transport dynamo with solar-like differenttial rotation. The Astrophysical Journal, 518, 508. doi:10.1086/307269.
[18] Leighton, R.B. (1969) A Magneto-Kinematic model of the solar cycle. The Astrophysical Journal, 156, 1. doi:10.1086/149943
[19] Sotavolta, O. (1947) The flight-tone (wing stroke frequency) of insects. Suomen Hy?nteistieteellinen Seura, 4, 1-117.
[20] Pringle, J.W. (1949) The excitation and contraction of the flight muscle of insects. Journal of Physiology, 108, 226- 232.
[21] Pringle, J.W. (1978) The Cronian Lecture, 1977: Stretch activation of muscle: Function and mechanism. Proceedings of the Royal Society B: Biological Science, 201, 107- 130.
[22] Merzendorfer, H. (2011) Mechanism for stretch activation proposed. Journal of Experimental Biology, 214, 4-5, doi:10.1242/jeb.049759.
[23] Snodgrass, R.E. (1935) Principles of insect morphology. McGraw-Hill Publishing Co., New York.
[24] Alcamo, I.E. and Krumhardt, B. (2004) Barron’s anatomy and physiology. Barron’s educational series.
[25] Chillemi, S., Barbi, M., Di Garbo, A., et al. (1997) Detection of nonlinearity in the healthy heart rhythm. Method of Information in Medicine, 36, 278-281.
[26] Chen, Z., Brown, E.N. and Barbgieri, R. (2008) Characterizing nonlinear heartbeat dynamics within a point process framework. IEEE Transactions on Biomedical Engineering, 57, 2781-2784. doi:10.1109/TBME.2010.2041002.
[27] Korhonen, I.K.J. and Turjanmaa, V.M.H. (1995) Second-order non-linearity of heart rate and blood pressure short- term variability. Computers in Cardiology, Lyon, 10-13 September 1995, 293-296.
[28] Guzzetti, S., Signorini, M.G., Cogliati, C., et al. (1996) Non-linear dynamics and chaotic indices in heart rate variability of normal subjects and heart transplanted patients. Cardiovascular Research, 31, 441-446.
[29] Perc, M. (2005) Nonlinear time series analysis of the human electrocardiogram. European Journal of Physics, 26, 757-768. doi:10.1088/0143-0807/26/5/008.
[30] Kuusela, T.E., Jarttii, T.T., Tahvanainen, K.U.O. and Kaila, T.J. (2002) Nonlinear methods of biosignal analysis in assessing terbutaline-induced heart rate and blood pressure changes. American Journal of Physiology: Heart and Circulatory Physiology, 282, H773-H781.
[31] Jo, J.A., Blasi, A., Valladares, E.M., et al. (2007) A nonlinear model of cardiac autonomic control in obstructive sleep apnea syndrome. Annals of Biomedical Engineering, 35, 1425-1443,
[32] Riedl, M., Suhrbier, A., Malberg, H., et al. (2008) Modeling the cardiovascular system using a nonlinear additive autoregressive model with exogenous input. Physical Re- view E, 78, 100919. doi:10.1103/PhysRevE.78.011919.
[33] Krans, J.L. (2010) The sliding filament theory of muscle contraction. Nature Education, 3, 66.
[34] Huxley, H.E. and Niedergerke, R. (1954) Structural changes in muscle during contraction: Interference microscopy of living muscle fibres. Nature, 173, 971-973.
[35] Huxley, H.E. and Hanson, J. (1954) Changes in the cross-striations of muscle during contraction and stretch and their structural interpretation. Nature, 173, 973-976.
[36] Hynes, T.R., et al. (1987) Movements of myosin fragments in vitro: Domains involved in force production. Cell, 48, 953-963. doi:10.1016/0092-8674(87)90704-5.
[37] Spudich, J.A. (2001) The myosin swinging cross-bridge model. Nature Reviews Molecular Cell Biology, 2, 387- 392. doi: 10.1038/35073086
[38] Starling, E.H., (1923) The Harveian oration on the “Wisdom of the Body”. Lancet, 202, 865-870.
[39] Linari, M., Reedy, M.K., Reedy, M.C., Lombardi, V. and Piazzesi, G. (2004) Ca-activation and stretch-activation in insect flight muscle. Biophysical Journal, 87, 1101-1111, doi:10.1529/biophysj.103.037374.
[40] Perz-Edwards, R.J., Irving, T.C., Baumann, B.A., et al. (2010) X-ray diffraction evidence for myosin-troponin connection and tropomyosin movement during stretch activation of insect flight muscle. Proceedings of the National Academy of Sciences of USA, 108, 120-125. doi:10.1073/pnas.1014599107.
[41] Campbell, K.B. and Chandra, M. (2006) Functions of stretch activation in heart muscle. The Journal of General Physiology, 127, 89-94. doi:10.1085/jgp.200509483.
[42] Solaro, R.J. (2007) Mechanisms of the frank-starling law of the heart: The beat goes on. Biophysical Journal, 93, 4095-4096. doi:10.1529/biophysj.107.117200.
[43] Allen, D.G. and Kentish, J.C. (1985) The cellular basis of the length-tension relation in cardiac muscle. Journal of Molecular and Cellular Cardiology, 17, 821-840.
[44] Steiger, G.J. (1971) Stretch activation and myogenic oscillation of isolated contractile structures of heart muscle. Pflugers Archiv, 330, 347-361.
[45] Steiger, G.J. (1977) Stretch-activation and tension transients in cardiac, skeletal and insect flight muscle. In: Tregear, Ed., Insect Flight Muscle, Elsevier, Amsterdam, 221-268.
[46] Vemuri, R., Lankford, E.B., Poetter, K., et al. (1999) The stretch-activation response may be critical to the proper functioning of the mammalian heart. Proceedings of the National Academy of Sciences of USA, 96, 1048-1053.
[47] Stelzer, J.E., Larsson, L., Fitzsimons, D.P. and Moss, R.L. (2006) Activation dependence of stretch-activation in mouse skinned myocardium: Implications for ventricular function. The Journal of General Physiology, 127, 95- 107. doi:101085/jgp.200509432.
[48] Fuchs, F. and Smith, S.H. (2001) Calcium, cross-bridges, and the Frank-Starling relationship. News in Physiological Science, 16, 5-10.
[49] Pearson, J.T., Shirai, M., Tsuchimochi, H., et al. (2007) Effects of sustained length-dependent activation on in situ cross-bridge dynamics in rat hearts. Biophysical Journal, 93, 4319-4329. doi:10.1529/biophysj.107.111740.
[50] Mayr, H.G, Mengel, J.G., Reddy, C.A., Chan, K.L. and Porter, H.S. (2000) Properties of QBO and SAO generated by gravity waves. Journal of Atmospheric and Solar- Terrestrial Physics, 62, 1135-1154. doi:101016/S1364-6826(00)00103-6.
[51] Mayr, H.G., Mengel, J.G., Chan, K.L. and Huang, F.T. (2010) Middle atmosphere dynamics with gravity wave interactions in the numerical spectral model: Zonal-mean variations. Journal of Atmospheric and Solar-Terrestrial Physics, 72, 807-826. doi:10.1016/j.jastp.2010.03.018

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.