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

View ORCID ProfileD.T. Pham, View ORCID ProfileZ.E. Musielak
doi: https://doi.org/10.1101/2022.03.25.485848
D.T. Pham
1Department of Biology, University of Texas at Arlington, Arlington, TX 76019, USA
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  • For correspondence: npham@mavs.uta.edu
Z.E. Musielak
2Department of Physics, University of Texas at Arlington, Arlington, TX 76019, USA
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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 discussed. It is suggested that the obtained standard Lagrangians can be used to identify physical similarities between different population models.

Competing Interest Statement

The authors have declared no competing interest.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted March 30, 2022.
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Lagrangian Formalism in Biology: I. Standard Lagrangians and their Role in Population Dynamics
D.T. Pham, Z.E. Musielak
bioRxiv 2022.03.25.485848; doi: https://doi.org/10.1101/2022.03.25.485848
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Lagrangian Formalism in Biology: I. Standard Lagrangians and their Role in Population Dynamics
D.T. Pham, Z.E. Musielak
bioRxiv 2022.03.25.485848; doi: https://doi.org/10.1101/2022.03.25.485848

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