On a geometric description of time dependent singular Lagrangians with applications to biological systems
Abstract
We consider certain analytical features of a stochastic model that can explain among other things competition among species and simultaneous predation on the competing species from a geometric perspective which allows for a systematic description of models admitting singular Lagrangians. The model equations are shown to admit a Jacobi Last Multiplier which in turn allows for the construction of a Lagrangian. The Lagrangian is of singular nature so that construction of the Hamiltonian via a Legendre transformation is not possible. A Hamiltonian description of the model therefore requires the introduction of Dirac brackets. Explicit results are presented for the "Kill the winner" model and its reductions.
Keywords
Cite
@article{arxiv.1908.09647,
title = {On a geometric description of time dependent singular Lagrangians with applications to biological systems},
author = {Sudip Garai and A Ghose-Choudhury and Partha Guha},
journal= {arXiv preprint arXiv:1908.09647},
year = {2021}
}
Comments
This is an updated and expanded version of an earlier draft arXiv:1908.09647v1[q-bio.PE] with more focus on geometric aspects