Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model

Symmetry

M.C. Nucci¹  G. Sanchini² 

[1] Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, 06123 Perugia, Italy E-Mail

关键词: Lie group analysis;    Jacobi last multiplier;    Lagrangians;    Noether’s theorem;    Easter Island population;   

DOI  :  10.3390/sym7031613

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.