We introduce an algorithm to find possible constants of motion for a given replicator equation. The algorithm is inspired by Dirac geometry and a Hamiltonian description for the replicator equations with such constants of motion, up to a time re-parametrization, is provided using Dirac$ \backslash $big-isotropic structures. Using the equivalence between replicator and Lotka-Volterra (LV) equations, the set of conservative LV equations is enlarged. Our approach generalizes the well-known use of gauge transformations to skew-symmetrize the interaction matrix of a LV system. In the case of predator-prey model, our method does allow interaction between different predators and between different preys.

中文翻译：

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Dirac \大各向同性结构下的守恒复制子和Lotka-Volterra方程

我们介绍一种算法，以查找给定复制器方程的可能运动常数。该算法的灵感来自狄拉克（Dirac）几何形状，并使用狄拉克（Dirac）\反斜杠（bigs）-大各向同性结构提供了具有这样的运动常数的汉密尔顿方程描述，其中包括这样的运动常数，直到时间重新参数化为止。利用复制器和Lotka-Volterra（LV）方程之间的等价关系，保守的LV方程组得以扩大。我们的方法概括了使用规范转换来倾斜对称化LV系统交互矩阵的方法。在捕食者－猎物模型的情况下，我们的方法确实允许不同捕食者之间以及不同猎物之间进行交互。