Novel Roles of Standard Lagrangians in Population Dynamics Modeling and Their Ecological Implications

The Lagrangian formalism based on the standard Lagrangians, which are characterized by the presence of the kinetic and potential energy-like terms, is established for selected population dynamics models. A general method that allows for constructing such Lagrangians is developed, and its specific applications are presented and discussed. The obtained results are compared with the previously found Lagrangians, whose forms were different as they did not allow for identifying the energy-like terms. It is shown that the derived standard Lagrangians for the population dynamics models can be used to study the oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. Moreover, other physical and biological insights that can be gained from the constructed standard Lagrangians are also discussed.