The normalization of dimensionless groups that rule the system of nonlinear coupled ordinary differential equations defined by the Lotka–Volterra biological or chemical oscillator has been derived in this work by applying a normalized nondimensionalization protocol. The normalization procedure, which is quite accurate, does not require complex mathematical steps; however, a deep physical understanding of the problem is required to choose the appropriate references to define the dimensionless variables. From the dimensionless groups derived, the functional dependences of some unknowns of interest are established. Due to the coupled nature of the problem that induces temporal concentration rates of each species that are quite different at each point of the phase diagram, this diagram has been divided into four stretches corresponding to the four quadrants. For each stretch, the limit values (maximum or minimum) of the variables, as well as their duration, are expressed in terms of the dimensionless groups derived before. Finally, to check all the mentioned dependences, a numerical simulation has been carried out.

中文翻译：

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使用归一化技术研究Lotka–Volterra生物或化学振荡器问题：时间和浓度的预测

在这项工作中，通过应用归一化的无量纲化协议，得出了无量纲的归一化规则，该无因次基数规范了由Lotka–Volterra生物或化学振荡器定义的非线性耦合常微分方程组。归一化过程非常准确，不需要复杂的数学步骤。但是，需要对问题有深刻的物理理解，才能选择适当的参考来定义无因次变量。从得出的无量纲组中，建立了一些未知量的功能依赖性。由于问题的耦合性质，导致每个物种的时间集中度在相图的每个点上都大不相同，此图已分为对应于四个象限的四个拉伸。对于每次拉伸，变量的极限值（最大值或最小值）及其持续时间均根据之前得出的无量纲组表示。最后，为了检查所有提到的依赖关系，进行了数值模拟。