Revisiting the Human and Nature Dynamics Model

    2020, Volume 25, Number 2, pp.  178-198

    Author(s): Grammaticos B., Willox R., Satsuma J.

    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
    Citation: Grammaticos B., Willox R., Satsuma J., Revisiting the Human and Nature Dynamics Model, Regular and Chaotic Dynamics, 2020, Volume 25, Number 2, pp. 178-198

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