Cite this paper
Min, K. (2013) A Stochastic Optimal Control Theory to Model Spontaneous Breathing. Applied Mathematics
, 1537-1546. doi: 10.4236/am.2013.411208
 A. L. Goldberger, “Heartbeats, Hormones, and Health: Is Variability the Spice of Life?” American Journal of Respiratory and Critical Care Medicine, Vol. 163, No. 6, 2001, pp. 1289-1290.http://dx.doi.org/10.1164/ajrccm.163.6.ed1801a
 N. S. Cherniack, G. S. Longobardo, O. R. Levine, R. Mellins and A. P. Fishman, “Periodic Breathing in Dogs,” Journal of Applied Physiology, Vol. 21, No. 6, 1966, pp. 1847-1854.
 U. Frey, M. Silverman, A. L. Barabási and B. Suki, “Irregularities and Power Law Distributions in the Breathing Pattern in Preterm and Term Infants,” Journal of Applied Physiology, Vol. 85, No. 3, 1998, pp. 789-797.
 B. Suki, “Fluctuations and Power Laws in Pulmonary Physiology,” American Journal of Respiratory and Critical Care Medicine, Vol. 166, No. 2, 2002, pp. 133-137. http://dx.doi.org/10.1164/rccm.200202-152PP
 K. J. Astroem, “Introduction to Stochastic Control Theory,” Dover Books on Electrical Engineering, New York, 1970.
 K. Min, K. Hosoi, Y. Kinoshita, S. Hara, H. Degami, T. Takada and T. Nakamura, “Use of Fractal Geometry to Propose a New Mechanism of Airway-Parenchymal Interdependence,” Open Journal of Molecular and Integrated Physiology, Vol. 2, No. 1, 2012, pp. 14-20. http://dx.doi.org/10.4236/ojmip.2012.21003
 K. Yasue, “Quantum Mechanics and Optimal Stochastic Control Theory,” Kaimei-shya, Tokyo, 2007 (in Japanese).
 B. Suki, N. Martinez, H. Parameswaran, A. Majumdar, R. Dellaca, C. Berry, J. J. Pillow and E. Bartolak-Suki, “Variability in the Respiratory System: Possible Origins And Implications,” B29, The Lung on the Border between Order and Chaos, 2012, p. A2682.
 J. G. Venegas, T. Winkler, G. Musch, M. F. Vidal Melo, D. Layfield, N. Tgavalekos, A. J. Fischman, R. J. Callahan, G. Bellani and R. S. Harris, “Self-Organized Patchiness in Asthma as a Prelude to Catastrophic Shifts,” Nature, Vol. 434, No. 7034, 2005, pp. 777-782.http://dx.doi.org/10.1038/nature03490
 G. S. Mitchell and S. M. Johnson, “Invited Review: Neuroplasticity in Respiratory Motor Control,” Journal of Applied Physiology, Vol. 94, No. 1, 2003, pp. 358-374.
 P. J. Fadel, S. M. Barman, S. W. Phillips and G. L. Gebber, “Fractal Fluctuations in Human Respiration,” Journal of Applied Physiology, Vol. 97, No. 6, 2004, pp. 20562064. http://dx.doi.org/10.1152/japplphysiol.00657.2004