Survival and weak chaos.

Sean Nee

doi:10.1098/rsos.172181

Abstract

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as ‘infant mortality’. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality—sensu engineering—without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.

Highlights

Ideas of chaos, as formally understood, had a significant impact on many sciences after the invention of computers
One of the first sciences to grasp the significance of such nonlinear dynamical behaviours was population biology, as a result of the work of May [1]
We will see how it arises for chaotic dynamical systems

Summary

Introduction

As formally understood, had a significant impact on many sciences after the invention of computers. One of the first sciences to grasp the significance of such nonlinear dynamical behaviours was population biology, as a result of the work of May [1] This made it understood that apparently random, and often large, fluctuations in a time series of organism abundance do not require explanations in terms of external perturbations or shocks to the system. The evolutionary ecology and reliability engineering of these units will enjoy the benefit of large streams of relevant data for the study of their performance, as we will sketch in the Discussion The collection of these data is accelerated by the demands of the industries associated with the evolution of cyber-physical systems including, for example, autonomous vehicles and many such technologies using Artificial Intelligence. These data are valuable as they are gathered on healthy systems which are functioning as the designers originally intended, like aircraft carrying black boxes

Classical framework

Models

The logistic map

The Pomeau–Manneville map

Findings

Infant mortality and burn-in