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Analysis of a generalized Fujikawa's growth model

机译：广义富士川增长模型分析

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摘要

We analyze a generalized form of the Fujikawas growth model which involves an adaptation function that enhances the representation of the lag phase. This model is autonomous, and combines a power law term, a saturation term and an adaptation function that suppresses the growth rate during initial period corresponding to the lag phase. The properties of the adaptation function arc determined, and the proposed model is examined separately for the regular measure and the logarithmic measure, including: Convergence and boundedness properties; population at the inflection point; conditions for the existence of the inflection point and lag phase; effect of model parameters on the existence of the inflection point and lag phase; population size of the inflection point under limiting values of the model parameters; and parameter values that lead to inflection point located at the mean value of the curve. Different combinations of model parameters lead to different possibilities for the existence of the inflection point and the lag phase. It was noticed that the power law term has a strong effect on the representation of the exponential growth phase, whereas the adaptation function has a strong effect on the representation of the lag phase. The lag phase duration depends on the exponent parameter of the adaptation function, and its dependence with respect to the power law parameter is low. Also, an approach is proposed for the analytical determination of the lag time, based on the application of the classical approach to a simplified model. Ascertained lag time values were obtained, what confirms the assumptions. At last, the model is applied to experimental data.
机译：我们分析了富士川生长模型的广义形式，涉及增强滞后阶段表示的适应功能。该模型是自主的，并结合电力法律项，饱和术语和适应功能，其抑制对应于滞后阶段的初始时段期间的生长速率。确定适应功能弧的特性，并分别检查所提出的模型，以进行规则测量和对数措施，包括：收敛和界限属性;拐点的人口;存在拐点和滞后阶段的条件;模型参数对拐点存在的影响;限制模型参数值下拐点的人口大小;导致位于曲线平均值的拐点的参数值。模型参数的不同组合导致拐点和滞后阶段存在的不同可能性。注意到权力律术语对指数增长阶段的表示具有很大的影响，而适应功能对滞后阶段的表示具有很强的影响。滞后阶段持续时间取决于适应功能的指数参数，其相对于电力法参数的依赖性低。此外，基于经典方法对简化模型的应用，提出了一种用于分析滞后时间的方法。获得了确定的滞后时间值，是什么证实假设。最后，该模型应用于实验数据。

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