Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model
Basener and Ross (2005) proposed a mathematical model that describes the dynamics of growth and sudden decrease in the population of Easter Island. We have applied Lie group analysis to this system and found that it can be integrated by quadrature if the involved parameters satisfy certain relations...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-09-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/7/3/1613 |
| _version_ | 1818038381115867136 |
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| author | M.C. Nucci G. Sanchini |
| author_facet | M.C. Nucci G. Sanchini |
| author_sort | M.C. Nucci |
| collection | DOAJ |
| description | Basener and Ross (2005) proposed a mathematical model that describes the dynamics of growth and sudden decrease in the population of Easter Island. We have applied Lie group analysis to this system and found that it can be integrated by quadrature if the involved parameters satisfy certain relationships. We have also discerned hidden linearity. Moreover, we have determined a Jacobi last multiplier and, consequently, a Lagrangian for the general system and have found other cases independently and dependently on symmetry considerations in order to construct a corresponding variational problem, thus enabling us to find conservation laws by means of Noether’s theorem. A comparison with the qualitative analysis given by Basener and Ross is provided. |
| first_indexed | 2024-12-10T07:41:50Z |
| format | Article |
| id | doaj.art-fdb7c224ac354b78afc0b7551943e067 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-12-10T07:41:50Z |
| publishDate | 2015-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-fdb7c224ac354b78afc0b7551943e0672022-12-22T01:57:17ZengMDPI AGSymmetry2073-89942015-09-01731613163210.3390/sym7031613sym7031613Symmetries, Lagrangians and Conservation Laws of an Easter Island Population ModelM.C. Nucci0G. Sanchini1Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, 06123 Perugia, ItalyDipartimento di Matematica e Informatica, Università degli Studi di Perugia, 06123 Perugia, ItalyBasener and Ross (2005) proposed a mathematical model that describes the dynamics of growth and sudden decrease in the population of Easter Island. We have applied Lie group analysis to this system and found that it can be integrated by quadrature if the involved parameters satisfy certain relationships. We have also discerned hidden linearity. Moreover, we have determined a Jacobi last multiplier and, consequently, a Lagrangian for the general system and have found other cases independently and dependently on symmetry considerations in order to construct a corresponding variational problem, thus enabling us to find conservation laws by means of Noether’s theorem. A comparison with the qualitative analysis given by Basener and Ross is provided.http://www.mdpi.com/2073-8994/7/3/1613Lie group analysisJacobi last multiplierLagrangiansNoether’s theoremEaster Island population |
| spellingShingle | M.C. Nucci G. Sanchini Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model Symmetry Lie group analysis Jacobi last multiplier Lagrangians Noether’s theorem Easter Island population |
| title | Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model |
| title_full | Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model |
| title_fullStr | Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model |
| title_full_unstemmed | Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model |
| title_short | Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model |
| title_sort | symmetries lagrangians and conservation laws of an easter island population model |
| topic | Lie group analysis Jacobi last multiplier Lagrangians Noether’s theorem Easter Island population |
| url | http://www.mdpi.com/2073-8994/7/3/1613 |
| work_keys_str_mv | AT mcnucci symmetrieslagrangiansandconservationlawsofaneasterislandpopulationmodel AT gsanchini symmetrieslagrangiansandconservationlawsofaneasterislandpopulationmodel |