On the fate of dynamical systems under a trade-off between cost and precision

TL;DR

This paper investigates how dynamical systems with processes balancing cost and precision evolve over time, identifying conditions for stable performance or deterioration, with implications for living organisms.

Contribution

It introduces a model analyzing the trade-off between cost and precision in dynamical systems, highlighting conditions leading to stability or deterioration.

Findings

Systems can maintain stability under certain cost-precision trade-offs

Error accumulation or resource decline leads to system deterioration

Implications for biological systems to avoid error buildup

Abstract

We analyze the fate of dynamical systems that consist of two kind of processes. The first type is supposed to perform a certain function by processing information at a required high accuracy, which is, however, limited to less than 100 percent, while the second process serves to maintain the required precision. Both processes are assumed to be subject to a trade-off between cost and precision, where the cost have to be paid from renewable but limited resources. In a discrete map we pursue the time evolution of errors and determine the conditions under which the fate of the system is either a stable performance at the desired accuracy, or a deterioration. Deterioration may be realized either as an accumulation of errors or a decline of resources when they are all absorbed for maintenance. We point to possible implications for living organisms and their perspectives to avoid an accumulation of errors in the course of time.