Modes of Growth in Dynamic Systems

TL;DR

This paper presents a unified framework for understanding growth modes in dynamic systems, linking thermodynamic responses, resource availability, and ecological models to explain diverse phenomena from rain formation to fish stock evolution.

Contribution

It introduces a theoretical model that constrains growth to distinct modes based on resource dynamics and connects physical and biological systems through predator-prey equations.

Findings

Growth modes depend on resource availability and energy constraints.

Growth and decay can be modeled using predator-prey equations.

The framework applies to phenomena like rain development and fish stock evolution.

Abstract

Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct modes that depend on the availability of material and energetic resources. These modes include a law of diminishing returns, logistic behavior and, if resources are expanding very rapidly, super-exponential growth. For a case where a system has a resolved sink as well as a source, growth and decay can be characterized in terms of a slightly modified form of the predator-prey equations commonly employed in ecology, where the perturbation formulation of these equations is equivalent to a damped simple harmonic oscillator. Thus, the framework presented here suggests a common theoretical under-pinning for emergent behaviors in the physical and life sciences. Specific examples are described for phenomena as seemingly dissimilar as the development of rain and the evolution of fish stocks.