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A Nonlinear ODE Model for a Consumeristic Society
Version 1
: Received: 22 March 2024 / Approved: 22 March 2024 / Online: 22 March 2024 (14:44:07 CET)
A peer-reviewed article of this Preprint also exists.
Badiale, M.; Cravero, I. A Nonlinear ODE Model for a Consumeristic Society. Mathematics 2024, 12, 1253. Badiale, M.; Cravero, I. A Nonlinear ODE Model for a Consumeristic Society. Mathematics 2024, 12, 1253.
Abstract
In this paper we introduce an ODE system to model the interaction between nature resources and human exploitation in a rich consumeristic society. In this model the rate of change of population depends on wealth per capita, and the rate of consumption has a quadratic growth with respect to population and wealth. As in our previous work \cite{BaCra_1}, we distinguish between renewable and non renewable resources, and we introduce a replenishment term for non renewable resources. We first get some information on the asymptotic behaviour of wealth and population, then we compute all the equilibria of the system and we study their stability when the parameter of exploitation of resources is small. Some numerical simulations confirm the theoretical results, and give suggestions for future research.
Keywords
Human and nature dynamics; ODE systems for society dynamics; Ecological- Economic Modeling
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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