We consider certain analytical features of the "Kill the Winner" model which is a stochastic model that can explain among other things competition among species and simultaneous predation on the competing species  . The model equations are shown to admit a Jacobi Last Multiplier which in turns 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  model and its reductions.
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.
D
the "Kill the Winner" model which is
A
from a geometric perspective which allows for a systematic description of models admitting singular Lagrangians
R
turns
turn
A
"Kill the winner"