Lagrangian structure of the two-dimensional Lotka-Volterra system
The two-dimensional Lotka-Volterra system describing the dynamics of self-regulating predator-prey ecosystems is studied. It is shown that this two-dimensional system has a Lagrangian structure with the Lagrangian linear in velocities and therefore singular but with unique dynamics. The constructive version of the Noether theorem is used to find the symmetries and first integrals to this system.
scientific article; zbMATH DE number 1337982