General Mathematics

    

A Dynamical Systems Model for Population and Depleting Resources

Authors: Samuel Forbes

We investigate a coupled, non-linear dynamical systems model for the relationship between population and depleting resources inspired by limits to growth. The model is determined by logistic growth in population with carrying capacity determined by resources. The rate of decline of resources is determined linearly by the population. The model produces an initial exponential increase in population followed by a decrease to the fixed point while congruently resources decrease in a sigmoidal fashion to the fixed point. We fit the model to world population over the period 10000 BC to 2021 in different time intervals corresponding to different growth rates. We show a number of projections to 2500 based on fitting to the time period of 1950 to 2021 with various parameter constraints.

Comments: 7 Pages.

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Submission history

[v1] 2024-10-11 10:50:03

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