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The development of largangians for biological models

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Abstract

A modern theory of the calculus of variations is used to form necessary and sufficient conditions for the existence of a Lagrangian representation of a system of first-order ordinary differential equations. There exists a theorem to the effect that when a system of ordinary differential equations is variationally self-adjoint, the fulfillment of such conditions is guaranteed. In addition, self-adjointness, allows establishement of an algorithm by which a Lagrangian for the system may be explicitly constructed. Examples in mathematical biology are given to illustrate the use of the stated theorem.

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Author notes

  1. Gregory H. Paine

    Present address: Department of Chemistry Baker Laboratory, Cornell University, Box 229, 14853, Ithaca, NY, USA

Authors and Affiliations

  1. Department of Physics, Washington University, 63130, St. Louis, MO, USA

    Gregory H. Paine

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  1. Gregory H. Paine
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Paine, G.H. The development of largangians for biological models. Bltn Mathcal Biology 44, 749–760 (1982). https://doi.org/10.1007/BF02465178

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  • DOI: https://doi.org/10.1007/BF02465178

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