Biology subjects

Musielak, Z. E.

Publications and source records attributed to Musielak, Z. E..

2 recordsLinked to original sources

bioRxiv2023

Lagrangian Formalism in Biology: II. Non-Standard and Null Lagrangians for Nonlinear Dynamical Systems and their Role in Population Dynamics

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and the limitations of this method are explored. It is shown that the limitations do not exist only for those nonlinear dynamical systems that can be converted into linear ones. The obtained results are applied to selected population dynamics models for which non-standard Lagrangians and their corresponding null Lagrangians and gauge functions are derived, and their roles in the population dynamics are discussed.

ecology↗

bioRxiv2022

Lagrangian Formalism in Biology: I. Standard Lagrangians and their Role in Population Dynamics

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 discussed. It is suggested that the obtained standard Lagrangians can be used to identify physical similarities between different population models.

ecology↗