2019/08/20 by Sudip Garai, Garai, Sudip, A Ghose-Choudhury +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Biological sciences #FOS: Physical sciences #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Microtubule and mitosis dynamics #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1908.09647
openalex publication_date 2019/08/20 · openalex created_date 2022/07/19 · openalex updated_date 2026/07/28
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.