By Anne Beuter, Leon Glass, Michael C. Mackey, Michele S. Titcombe
This booklet bargains with the applying of arithmetic in modeling and knowing physiological structures, specifically these concerning rhythms. it truly is divided approximately into sections. within the first a part of the booklet, the authors introduce rules and strategies from nonlinear dynamics which are appropriate to the research of organic rhythms. the second one half includes 5 in-depth case reviews during which the authors use the theoretical instruments constructed previous to enquire a few physiological approaches: the dynamics of excitable nerve and cardiac tissue, resetting and entrainment of organic oscillators, the results of noise and time hold up at the scholar gentle reflex, pathologies linked to blood mobilephone replication, and Parkinsonian tremor. One novel characteristic of the publication is the inclusion of classroom-tested computing device workouts all through, designed to shape a bridge among the mathematical idea and physiological experiments.
This ebook might be of curiosity to scholars and researchers within the common and actual sciences eager to find out about the complexities and subtleties of physiological platforms from a mathematical perspective.
The authors are contributors of the Centre for Nonlinear Dynamics in body structure and medication. the fabric during this e-book used to be built to be used in classes and used to be awarded in 3 summer time faculties run through the authors in Montreal.
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Extra info for Nonlinear Dynamics in Physiology and Medicine
A-D) 2 +4BC >O and JA + Dj < IJ(A- D) 2 + 4BC,. In this case, the eigenvalues are both real, but with different signs. Glucose tolerance test We illustrate the dynamics in two-dimensional ordinary differential equations by considering the glucose tolerance test. Diabetes mellitus is a disease of metabolism that is characterized by too much sugar (glucose) in the blood and urine. A diabetic's body is unable to burn off its carbohydrates because of an insufficient, or ineffective, supply of insulin.
Thanks to S. Bernard for generating this figure. differential equation. Imagine a two-dimensional plane that cuts across the cycle. Consider the point where the cycle cuts t hrough the plane. After integrating the differential equation for a le ngth of time that is equal to the period of the cycle, the point will once again return to the intersection of the cycle and the plane. Consider, however, other points in the plane in a neighborhood of the cycle. Assume that when the equations of motion are integrat ed, each of these points returns to the plane and that ali trajectories transversely cross the plane.
L; and niter is the number of iterations. The output is a vector y of length niter containing the iterated values. 1,4,100); testper(y,epsilon,maxper) This program determines whether there is a periodic orbit in the sequence given by the vector y whose period is less than or equal to maxper. The convergence criterion is that two iterates of y are closer than epsilon. The output is the period per. If no convergence is found the output is -1. L between mubegin and muend. cobweb(function, xzero,mu,niter) This program iterates the specified finite-difference equation and displays the cobweb diagram.
Nonlinear Dynamics in Physiology and Medicine by Anne Beuter, Leon Glass, Michael C. Mackey, Michele S. Titcombe