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.
Keywords:
population dynamics, dynamical systems, collapse, resources and reserves, discretisation, generalised cellular automaton.
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.
Citation:
Basil Grammaticos, Ralph Willox, Junkichi Satsuma, “Revisiting the Human and Nature Dynamics Model”, Regul. Chaotic Dyn., 25:2 (2020), 178–198
\Bibitem{GraWilSat20}
\by Basil Grammaticos, Ralph Willox, Junkichi Satsuma
\paper Revisiting the Human and Nature Dynamics Model
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 2
\pages 178--198
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\crossref{https://doi.org/10.1134/S1560354720020045}
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https://www.mathnet.ru/eng/rcd1058
https://www.mathnet.ru/eng/rcd/v25/i2/p178
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F. Meloni, G. M. Nakamura, B. Grammaticos, A. S. Martinez, M. Badoual, “Modeling Cooperation and Competition in Biological Communities”, Rus. J. Nonlin. Dyn., 19:3 (2023), 333–358
Meir Shillor, Thanaa Ali Kadhim, “Analysis and simulations of the HANDY model with social mobility, renewables and nonrenewables”, ejde, 2023:01-?? (2023), 59
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G. Nakamura, S. Plaszczynski, B. Grammaticos, M. Badoual, “Modelling the Effect of Virulent Variants with SIR”, Rus. J. Nonlin. Dyn., 17:4 (2021), 475–490
G Nakamura, B Grammaticos, M Badoual, “Vaccination strategies for a seasonal epidemic: a simple SIR model”, Open Communications in Nonlinear Mathematical Physics, Volume 1 (2021)
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