Non-Standard and Null Lagrangians for Nonlinear Dynamical Systems and Their Role in Population Dynamics

Diana T. Pham () and Zdzislaw E. Musielak
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Diana T. Pham: Department of Biology, University of Texas at Arlington, Arlington, TX 76019, USA
Zdzislaw E. Musielak: Department of Physics, University of Texas at Arlington, Arlington, TX 76019, USA

Mathematics, 2023, vol. 11, issue 12, 1-15

Abstract: 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.

Keywords: ordinary differential equations; mathematical biology; nonlinear dynamical systems; non-standard Lagrangian; ecological model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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