Revisiting the Human and Nature Dynamics model

TL;DR

This paper introduces a simple differential equation-based model to study the interaction between human populations and natural resources, revealing complex dynamics including steady states, oscillations, and potential collapse.

Contribution

It presents a novel, discretized and cellular automaton-like formulation of the human-nature interaction model, highlighting possible collapse scenarios.

Findings

Rich dynamical behaviors including steady states, oscillations, and collapse.

Collapse or societal transfiguration is a possible outcome under certain conditions.

The model's dynamics are highly sensitive to parameter choices.

Abstract

We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of ordinary differential equations, which are subsequently discretised, the discrete system providing a natural integrator for the continuous one. An ultradiscrete, generalised cellular automaton-like, model is also derived. The dynamics of our simple, three-component, model are particularly rich exhibiting either a route to a steady state or an oscillating, limit cycle-type regime or to a collapse. While these dynamical behaviours depend strongly on the choice of the details of the model, the important conclusion is that a collapse or near collapse, leading to the disappearance of the population or to a complete transfiguration of its societal model, is indeed possible.