Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model
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 variab...
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| Language: | English |
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MDPI AG
2025-05-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/6/430 |
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| author | Marino Badiale Isabella Cravero |
| author_facet | Marino Badiale Isabella Cravero |
| author_sort | Marino Badiale |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6db821a85efd40b9b65e2ec0a5086af4 |
| institution | Matheson Library |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-6db821a85efd40b9b65e2ec0a5086af42025-06-25T13:28:16ZengMDPI AGAxioms2075-16802025-05-0114643010.3390/axioms14060430Interactions Between Wealth and Natural Resources: A Nonlinear ODE ModelMarino Badiale0Isabella Cravero1Department of Mathematics, University of Turin, 10123 Torino, ItalyDepartment of Mathematics, University of Turin, 10123 Torino, ItalyIn 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.https://www.mdpi.com/2075-1680/14/6/430human and nature dynamicsODE systems for society dynamicsecological–economic modelingsustainability analysisnonlinear dynamical systems |
| spellingShingle | Marino Badiale Isabella Cravero Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model Axioms human and nature dynamics ODE systems for society dynamics ecological–economic modeling sustainability analysis nonlinear dynamical systems |
| title | Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model |
| title_full | Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model |
| title_fullStr | Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model |
| title_full_unstemmed | Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model |
| title_short | Interactions Between Wealth and Natural Resources: A Nonlinear ODE Model |
| title_sort | interactions between wealth and natural resources a nonlinear ode model |
| topic | human and nature dynamics ODE systems for society dynamics ecological–economic modeling sustainability analysis nonlinear dynamical systems |
| url | https://www.mdpi.com/2075-1680/14/6/430 |
| work_keys_str_mv | AT marinobadiale interactionsbetweenwealthandnaturalresourcesanonlinearodemodel AT isabellacravero interactionsbetweenwealthandnaturalresourcesanonlinearodemodel |