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Non-Standard and Null Lagrangians for Nonlinear Dynamical Systems and their Role in Population Dynamics
Version 1
: Received: 27 April 2023 / Approved: 28 April 2023 / Online: 28 April 2023 (04:49:37 CEST)
A peer-reviewed article of this Preprint also exists.
Pham, D.T.; Musielak, Z.E. Non-Standard and Null Lagrangians for Nonlinear Dynamical Systems and Their Role in Population Dynamics. Mathematics 2023, 11, 2671. Pham, D.T.; Musielak, Z.E. Non-Standard and Null Lagrangians for Nonlinear Dynamical Systems and Their Role in Population Dynamics. Mathematics 2023, 11, 2671.
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
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.
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