Lagrangians for Biological Models

DOI

10.1142/S1402925112500210How to use a DOI?

Keywords

Jacobi Last Multiplier; Lagrangian; population dynamics

Abstract

We show that a method presented in [S. L. Trubatch and A. Franco, Canonical Procedures for Population Dynamics, J. Theor. Biol. 48 (1974) 299–324] and later in [G. H. Paine, The development of Lagrangians for biological models, Bull. Math. Biol. 44 (1982) 749–760] for finding Lagrangians of classic models in biology, is actually based on finding the Jacobi Last Multiplier of such models. Using known properties of Jacobi Last Multiplier we show how to obtain linear Lagrangians of systems of two first-order ordinary differential equations and nonlinear Lagrangian of the corresponding single second-order equation that can be derived from them, even in the case where those authors failed such as the host-parasite model. Also we show that the Lagrangians of certain second-order ordinary differential equations derived by Volterra in [V. Volterra, Calculus of variations and the logistic curve, Hum. Biol. 11 (1939) 173–178] are particular cases of the Lagrangians that can be obtained by means of the Jacobi Last Multiplier. Actually we provide more than one Lagrangian for those Volterra's equations.

Copyright

© 2012 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - M. C. Nucci
AU  - K. M. Tamizhmani
PY  - 2012
DA  - 2012/09/20
TI  - Lagrangians for Biological Models
JO  - Journal of Nonlinear Mathematical Physics
SP  - 330
EP  - 352
VL  - 19
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500210
DO  - 10.1142/S1402925112500210
ID  - Nucci2012
ER  -