Physiological Singularities Modeled by Nondeterministic Equations of Motion and the Effect of Noise

  • Joseph P. Zbilut
  • Alfred Hübler
  • Charles L. WebberJr.
Part of the Institute for Nonlinear Science book series (INLS)


Much interest has been expressed in applying nonlinear dynamics to model the apparently complex dynamics of physiological systems. Many assertions in this regard, however, fail on the basis of (i) mathematical assumptions and (ii) basic understanding of the physiology involved. Specifically, our preliminary research using experimental data from breathing patterns as well as electrocardiographic signals suggests that the dynamics can often be modeled as a nondeterrninistic oscillator whose equations of motion do not satisfy the Lipschitz condition for all values of x, that is, there may exist an infinite number of solutions (one trajectory at a time), which are not unique. This property, in fact, often confuses these dynamics with deterministic chaos. Furthermore, analysis of nondeterministic singularities suggests the possibility of controlling resulting trajectories with relatively little effort due to sensitivities to noise and other modulations. In sum, the traditional approach in science has been based on causality and determinism complicated with noise. The present study suggests that biological systems are based on randomness and nondeterminism complicated by a little bit of causality, to achieve concurrent flexibility and stability.


Chaotic Dynamic Physiological System Breathing Cycle Inertial Manifold Deterministic Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Joseph P. Zbilut
  • Alfred Hübler
  • Charles L. WebberJr.

There are no affiliations available

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