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.
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Acknowledgements
The authors would like to acknowledge most stimulating discussions with A. Ramani. R. Willox would like to acknowledge support from the Japan Society for the Promotion of Science (JSPS), through the JSPS grant: KAKENHI grant number 18K03355.
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Grammaticos, B., Willox, R. & Satsuma, J. Revisiting the Human and Nature Dynamics Model. Regul. Chaot. Dyn. 25, 178–198 (2020). https://doi.org/10.1134/S1560354720020045
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DOI: https://doi.org/10.1134/S1560354720020045
Keywords
- population dynamics
- dynamical systems
- collapse
- resources and reserves
- discretisation
- generalised cellular automaton