标题： 生物模型的拉格朗日量 显示英文标题

标题： Lagrangians for biological models

摘要： 我们证明了在[S.L. Trubatch和A. Franco, 生物种群动力学的规范程序, J. Theor. Biol. 48 (1974), 299-324]以及后来在[G.H. Paine, 生物模型拉格朗日量的发展, Bull. Math. Biol. 44 (1982) 749-760]中提出的方法, 用于寻找生物学经典模型的拉格朗日量, 实际上是基于寻找这些模型的雅可比最后乘数。利用雅可比最后乘数已知的性质, 我们展示了如何获得这些一阶系统的线性拉格朗日量以及可以从它们导出的相应单个二阶方程的非线性拉格朗日量, 即使在这些作者未能做到的情况下, 如寄主-寄生模型。 显示英文摘要

摘要： We show that a method presented in [S.L. Trubatch and A. Franco, Canonical Procedures for Population Dynamics, J. Theor. Biol. 48 (1974), 299-324] and later in [G.H. Paine, The development of Lagrangians for biological models, Bull. Math. Biol. 44 (1982) 749-760] for finding Lagrangians of classic models in biology, is actually based on finding the Jacobi Last Multiplier of such models. Using known properties of Jacobi Last Multiplier we show how to obtain linear Lagrangians of those first-order systems and nonlinear Lagrangian of the corresponding single second-order equations that can be derived from them, even in the case where those authors failed such as the host-parasite model.