含时奇异拉格朗日量的几何描述及其在生物系统中的应用
On a geometric description of time dependent singular Lagrangians with applications to biological systems
摘要：
我们认为某些分析功能的随机模型，可以解释除其他事项外，物种之间的竞争和同时捕食的竞争物种从几何的角度，允许系统的描述模型承认奇异拉格朗日。模型方程示出承认一个雅可比最后乘子，这反过来又允许建设的拉格朗日。拉格朗日量是奇异的性质，因此通过勒让德变换的哈密顿量的建设是不可能的。因此，模型的哈密顿描述需要引入狄拉克括号。明确的结果，提出了“杀死赢家”模型及其减少。
英文摘要：
We consider certain analytical features of a stochastic model that can explain among other things competition among species and simultaneous predation on the competing species from a geometric perspective which allows for a systematic description of models admitting singular Lagrangians. The model equations are shown to admit a Jacobi Last Multiplier which in turn allows for the construction of a Lagrangian. The Lagrangian is of singular nature so that construction of the Hamiltonian via a Legendre transformation is not possible. A Hamiltonian description of the model therefore requires the introduction of Dirac brackets. Explicit results are presented for the "Kill the winner" model and its reductions.
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