The authors construct a singular Lagrangian and Dirac-bracket Hamiltonian for the Kill the Winner model, but the resulting phase-space dynamics is trivial and contradicts the ecological equations.
Goriely, Integrability and nonintegrability of dynamical systems
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On a geometric description of time dependent singular Lagrangians with applications to biological systems
The authors construct a singular Lagrangian and Dirac-bracket Hamiltonian for the Kill the Winner model, but the resulting phase-space dynamics is trivial and contradicts the ecological equations.