Skip to main content
SpringerLink
Log in

Poincare Return Maps

  • Chapter
  • First Online:
Trajectory Analysis in Health Care

  • 739 Accesses

Abstract

The Poincare return map is a model for measuring changes in trajectories and for evaluating the effects of forces that facilitate or present barriers to the pathways. It is important to measure the stability of a trajectory or its deviation. With either situation, one seeks to understand the variables that maintain stability or that generate the deviation. Then, we can experiment with manipulation of the variables to return a deviated pathway to stability or to jump an aberrant stable pathway to an altered stable trajectory that is closer to better health.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

PQRST:

Electrocardiogram peaks and troughs for heart wavelike contractions

PTSD:

Post traumatic stress disorder

References

  • Agutter, P. S., & Tuszynski, J. A. (2011). Analytic theories of allometric scaling. The Journal of Experimental Biology, 214, 1055–1062.

    Article  Google Scholar 

  • Bash, F.N. (1986). Present, past and future velocity of nearby stars: The path of the sun in 108 years.’ In R. Smoluchowshi, J.N. Bahcall, and M.S. Matthews (Eds.), The Galaxy and the solar system (p. 35). Tucson: University of Arizona Press.

    Google Scholar 

  • Beck, W. S., Liem, K. F., & Simpson, G. G. (1991). Life: An introduction to biology (3rd ed.). New York: HarperCollins.

    Google Scholar 

  • Bracewell, R. (1965). The Fourier transform and its applications. New York: McGraw-Hill.

    Google Scholar 

  • Bracewell, R. (1988). Spectral analysis of the Elatina varve series. Stanford, CA: Stanford University Center for space science and astrophysics, document CSSA-ASTRO-88-13.

    Google Scholar 

  • Bracewell, R. (1989). The Fourier transform. Scientific American, 260(6), 86–95.

    Article  CAS  Google Scholar 

  • Christian, J. J., Flyger, V., & Davis, D. E. (1960). Factors in the mass mortality of a herd of Sika deer, Cervus nippon. Chesapeake Science, 1(2), 79–95.

    Article  Google Scholar 

  • Curtis, H., & Barnes, N. S. (1994). Invitation to biology (5th ed.). New York: Worth Publishers.

    Google Scholar 

  • Davies, P., Demetrius, L. A., & Tuszynski, J. A. (2012). Implications of quantum metabolism and natural selection for the origin of cancer cells and tumor progression. AIP Advances, 2, 011101. http://dx.doi.org/10.1063/1.3697850.

    Article  PubMed Central  Google Scholar 

  • Dyson, F. (2004). A meeting with Enrico Fermi. Nature, 427, 297.

    Article  CAS  PubMed  Google Scholar 

  • Feynman, R. P. (1948). Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics, 20(2), 367–387.

    Article  Google Scholar 

  • Feynman, R. (1988). QED: The strange theory of light and matter. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Frisch, P. C. (1993). G-star astropauses: A test for interstellar pressure. The Astrophysical Journal, 407, 198–206.

    Article  Google Scholar 

  • GBD 2015 Mortality and Causes of Death Collaborators. (2016). Global, regional, and national life expectancy, all-cause mortality, and cause-specific mortality for 249 causes of death, 1980-2015: A systematic analysis for the global burden of disease study 2015. The Lancet, 388(10053), 1459–1544.

    Article  Google Scholar 

  • Granada, A., Hennig, M., Ronacher, B., Kramer, A., & Herzel, H. (2009). Phase response curves: Elucidating the dynamics of coupled oscillators. Methods in Enzymology, 454, 1–27.

    Article  CAS  PubMed  Google Scholar 

  • Hitzl, D. L. (1975). The swinging spring – Invariant curves formed by quasi-periodic solutions. III. Astronomy & Astrophysics, 41, 187–198.

    Google Scholar 

  • Hollar, D. (2013). Cross-sectional patterns of allostatic load among persons with varying disabilities, NHANES: 2001-2010. Disability and Health Journal, 6, 177–187.

    Article  PubMed  Google Scholar 

  • Hollar, D., & Lewis, J. (2015). Heart age differentials and general cardiovascular risk profiles for persons with varying disabilities: NHANES 2001-2010. Disability and Health Journal, 8, 51–60. http://dx.doi.org/10.1016/j.dhjo.2014.07.007.

  • Hollar, D. (2015). Evaluating the interface of health data and policy: Applications of geospatial analysis to county-level national data. Children's Health Care, 45(3), 266-285. http://dx.doi.org/10.1080/02739615.2014.996884

  • Hollar, D. (2016). Lifespan development, instability, and Waddington’s epigenetic landscape. In D. Hollar (Ed.), Epigenetics, the environment, and children’s health across lifespans (pp. 361–376). New York: Springer.

    Chapter  Google Scholar 

  • Hollar, D. (2017). Biomarkers of chondriome topology and function: Implications for the extension of healthy aging. Biogerontology. doi:10.1007/s10522-016-9673-5.

  • Iovane, G., Laserra, E., & Tortoriello, F.S. (2003). Stochastic self-similar and fractal universe. arXiv:astro-ph/0308370v1 21 Aug 2003.

    Google Scholar 

  • Krebs, C. J. (1978). Ecology: The experimental analysis of distribution and abundance (2nd ed.). New York: Harper & Row.

    Google Scholar 

  • Kumar, R., Clermont, G., Vodovotz, Y., & Chow, C. C. (2004). The dynamics of acute inflammation. Journal of Theoretical Biology, 230, 145–155.

    Article  CAS  PubMed  Google Scholar 

  • Levitin, D. J., Chordia, P., & Menon, V. (2012). Musical rhythm spectra from Bach to Joplin obey a 1/f power law. Proceedings of the National Academy of Sciences USA, 109(10), 3716–3720.

    Article  CAS  Google Scholar 

  • Lévy-Leblond, J.-M., & Balibar, F. (1990). Quantics: rudiments of quantum physics. New York: North-Holland.

    Google Scholar 

  • Liu, Y.-Y., Slotine, J.-J., & Barabási, A.-L. (2011). Controllability of complex networks. Nature, 473, 167–173.

    Article  CAS  PubMed  Google Scholar 

  • Lotka, A. J. (1956). Elements of mathematical biology. New York: Dover.

    Google Scholar 

  • Loy, G. (2007). Musimathics: The mathematical foundations of music (Vol. 2). Cambridge, MA: MIT Press.

    Google Scholar 

  • Malhotra, R. (1998). Orbital resonances and chaos in the solar system. Solar System Formation and Evolution, 149, 37–63.

    Google Scholar 

  • National Center for Health Statistics. (2012). Healthy people 2010 final review. Hyattsville, MD: U.S. Department of Health and Human Services.

    Google Scholar 

  • Perdang, J. (1983). Kolmogorov unstable stellar oscillations. Solar Physics, 82, 297–321.

    Article  Google Scholar 

  • Rolfs, C. E., & Rodney, W. S. (1988). Cauldrons in the cosmos: Nuclear astrophysics. Chicago: University of Chicago Press.

    Google Scholar 

  • Smith, R. L., & Smith, T. M. (1998). Elements of ecology (4th ed.). Menlo Park, CA: Benjamin/Cummings.

    Google Scholar 

  • The Lancet. (2016). The global burden of disease study 2015. The Lancet, 388(10053), 1447–1850.

    Article  CAS  Google Scholar 

  • Thom, R. (1972). Structural stability and morphogenesis: An outline of a general theory of models. New York: W.A. Benjamin/Westview.

    Google Scholar 

  • Verveen, A. A., & Derksen, H. E. (1968). Fluctuation phenomena in nerve membrane. Proceedings of the IEEE, 56, 906–916.

    Article  Google Scholar 

  • Walker, G. H., & Ford, J. (1969). Amplitude instability and ergodic behavior for conservative nonlinear oscillator systems. Physical Review, 188, 416–432.

    Article  Google Scholar 

  • Weisstein, E.W. (2016). Resonance overlap. Wolfram MathWorld. Accessed 20 March 2016 at http://mathworld.wolfram.com/ResonanceOverlap.html.

  • Wisdom, J., & Peale, S. J. (1984). The chaotic rotation of Hyperion. Icarus, 58, 137–152.

    Article  Google Scholar 

  • Wright, S. (1934). The method of path coefficients. Annals of Mathematical Statistics, 5, 161–215.

    Article  Google Scholar 

  • Wright, S. (1960). Path coefficients and path regressions: Alternative or complementary concepts? Biometrics, 16(2), 189–202.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Health Administration, Pfeiffer University, Morrisville, North Carolina, USA

    David W. Hollar

Authors
  1. David W. Hollar
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Cite this chapter

Hollar, D.W. (2018). Poincare Return Maps. In: Trajectory Analysis in Health Care. Springer, Cham. https://doi.org/10.1007/978-3-319-59626-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59626-6_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59625-9

  • Online ISBN: 978-3-319-59626-6

  • eBook Packages: MedicineMedicine (R0)

Publish with us

Policies and ethics

Search

Navigation