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Volume 14
Issue 6
10.3390/axioms14060430
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Article

Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model

by
Marino Badiale
and
Isabella Cravero
*
Department of Mathematics, University of Turin, 10123 Torino, Italy
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(6), 430; https://doi.org/10.3390/axioms14060430 (registering DOI)
Submission received: 5 May 2025 / Revised: 28 May 2025 / Accepted: 30 May 2025 / Published: 30 May 2025
(This article belongs to the Section Mathematical Analysis)
Versions Notes

Abstract

In this paper we study an ODE model for the interaction between nature and society where the system dynamics is driven largely by the social wealth. The relevant variables are renewable resources, non-renewable ones, and wealth, while population depends on wealth and does not act on the other variables. We first obtain that the relevant trajectories are positive and cannot grow arbitrarily large. Then we compute all the equilibria and study their stability. We also give numerical simulations of some trajectory.
Keywords: human and nature dynamics; ODE systems for society dynamics; ecological–economic modeling; sustainability analysis; nonlinear dynamical systems human and nature dynamics; ODE systems for society dynamics; ecological–economic modeling; sustainability analysis; nonlinear dynamical systems

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MDPI and ACS Style

Badiale, M.; Cravero, I. Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model. Axioms 2025, 14, 430. https://doi.org/10.3390/axioms14060430

AMA Style

Badiale M, Cravero I. Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model. Axioms. 2025; 14(6):430. https://doi.org/10.3390/axioms14060430

Chicago/Turabian Style

Badiale, Marino, and Isabella Cravero. 2025. "Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model" Axioms 14, no. 6: 430. https://doi.org/10.3390/axioms14060430

APA Style

Badiale, M., & Cravero, I. (2025). Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model. Axioms, 14(6), 430. https://doi.org/10.3390/axioms14060430

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