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

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.