Delay-Induced Uncertainty in Physiological Systems

Medical practice in the intensive care unit is based on the supposition that physiological systems such as the human glucose-insulin system are reliabile. Reliability of dynamical systems refers to response to perturbation: A dynamical system is reliable if it behaves predictably following a perturbation. Here, we demonstrate that reliability fails for an archetypal physiological model, the Ultradian glucose-insulin model. Reliability failure arises because of the presence of delay. Using the theory of rank one maps from smooth dynamical systems, we precisely explain the nature of the resulting delay-induced uncertainty (DIU). We develop a recipe one may use to diagnose DIU in a general dynamical system. Guided by this recipe, we analyze DIU emergence first in a classical linear shear flow model and then in the Ultradian model. Our results potentially apply to a broad class of physiological systems that involve delay.

IMPROVED CANONICAL QUANTIZATION METHOD OF SPINOR ELECTRODYNAMICS WITH SINGULAR LAGRANGIAN

This paper analyzes the general interaction of spinor field and electromagnetic field, i.e. spinor electrodynamics with singular Lagrangian, and the improved canonical quantization method of spinor electrodynamics is given in order to overcome the problems of the second-class constraint linear combination and the first-class constraint number maximization brought by the traditional canonical quantization method. In the improved canonical quantization method, there are no problems of artificial linear combination and first-class constraint number maximization, at the same time, the stability of the system is considered. The improved canonical quantization method is more natural than the traditional way and we show that the results of the canonical quantization of spinor electrodynamics are equal to the results of the traditional way. For a general dynamical system with singular Lagrangian, one can extendingly use the improved canonical quantization method to quantize the system.

A NO-CHAOS THEOREM FOR NON-MINIMALLY COUPLED SCALAR FIELD COSMOLOGY AND A NEW COSMOGENESIS SCENARIO

A general dynamical system approach to classical self-consistent scalar field cosmology is presented in the framework of spatially flat FLRW space–times, for arbitrary potentials and arbitrary non-minimal coupling. We show that these universes cannot undergo chaotic behaviors, thus suggesting a possible new role of inflation in cosmology. An unexpectedly involved topology of the phase-portrait of the cosmological dynamics is exhibited: Dynamically forbidden regions, playing a crucial dynamical role, appear. A new exact critical solution, a heteroclinic orbit, connects two de Sitter inflationary regimes. We suggest a novel intriguing semiclassical cosmogenesis scenario in which the quantized scalar field could tunnel through the classically forbidden region, from the Minkowski space–time towards the nearest classically allowed solution: The critical one.