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Jacobian Matrices and Lyapunov Exponents

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Trajectory Analysis in Health Care

Abstract

The Lyapunov exponent λ represents a measure of stable or unstable change in the nonlinear behavior of systems. This exponent can be calculated as the real components of the eigenvalue solutions to the differential equations describing a system. They can be linked to transition points between single period and period doubling events in bifurcation diagrams as a system changes its periodicity; such behavior ultimately leads to the transition points for chaotic behavior. The measure provides relevant applications for mapping dynamic changes in health and medicine. Zurek describes this process as the stretching and squeezing of a dynamical system, simultaneous with the decoherence and regained coherence, respectively, of a wavefunction.

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Abbreviations

Det:

Determinant

HLA:

Human leukocyte antigen

MHC:

Major histocompatibility complex

PRC:

Phase response curve

TNF:

Tumor necrosis factor

TRAIL:

TNF apoptosis inducing ligand

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Authors and Affiliations

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

    David W. Hollar

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  1. David W. Hollar
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Hollar, D.W. (2018). Jacobian Matrices and Lyapunov Exponents. In: Trajectory Analysis in Health Care. Springer, Cham. https://doi.org/10.1007/978-3-319-59626-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-59626-6_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59625-9

  • Online ISBN: 978-3-319-59626-6

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