Pham, D.T.; Musielak, Z.E. Novel Roles of Standard Lagrangians in Population Dynamics Modeling and Their Ecological Implications. Mathematics2023, 11, 3653.
Pham, D.T.; Musielak, Z.E. Novel Roles of Standard Lagrangians in Population Dynamics Modeling and Their Ecological Implications. Mathematics 2023, 11, 3653.
Pham, D.T.; Musielak, Z.E. Novel Roles of Standard Lagrangians in Population Dynamics Modeling and Their Ecological Implications. Mathematics2023, 11, 3653.
Pham, D.T.; Musielak, Z.E. Novel Roles of Standard Lagrangians in Population Dynamics Modeling and Their Ecological Implications. Mathematics 2023, 11, 3653.
Abstract
The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.
Keywords
standard lagrangian; calculus of variation; hamiltonian; Lagrangian formalism; population dynamics; Euler-Lagrange equation; mathematical biology; nonlinear dynamical systems; ecological model
Subject
Biology and Life Sciences, Ecology, Evolution, Behavior and Systematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
