In this paper, a theoretical model has been proposed for the first time to illustrate the living Tulsi (Holy Basil) leaf evolution in describing the branching systems in the intermediate range of frequencies. The proposed fitting function following the applied model portrays the whole stages of the temporal evolution of Tulsi (Holy Basil, “Ocimumtenuiflorum”) leaf during the six days of impedance measurements with a high degree of accuracy (with fitting error less than 0.1 percent). The developed fitting parameter enables to identify the three stages of temporal evaluation of the Tulsi leaf as “vital leaf activity” (first stage), “quasi-chaotic behaviour” (second stage), and the “dying” (third stage). The theoretical model proposed in this work incorporated a fractal element having complex conjugated power law of exponents and a fractal element with a time lagged branching process. This novel approach introduces an additional degree of freedom over the previously proposed impedance models in terms of its imaginary part of complex conjugated power-law exponent. Further, it increases flexibility and versatility in accurately modeling the behavioral variations of complex branching systems, whose seemingly nondeterministic temporal nature had been considered earlier as counterintuitive and random. The incorporation of branching processes in comprehensively explaining the complex biological systems allows us to gain a deeper insight into the transfer of charge processes in the intermediate range of available frequency scales. Furthermore, the proposed model validates the presence of new fractal elements with a complex conjugated power law of exponents in naturally occurring biological processes. The experimental confirmation can play a key role in explaining a wide class of branching processes in complex systems and enrich the modern theory of fractional calculus.

中文翻译：

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复杂生物系统中自相似/分支过程的检测：图尔西（圣罗勒）叶“cimumtenuiflorum”阻抗测量值的时间演化分析


在本文中，首次提出了一个理论模型来说明活的圣罗勒叶在描述中频率范围内的分枝系统时的演化。应用模型提出的拟合函数以高精度（拟合误差小于 0.1%）描绘了在六天的阻抗测量期间 Tulsi（圣罗勒，“Ocimumtenuiflorum”）叶子的时间演化的整个阶段。开发的拟合参数能够识别图尔西叶时间评估的三个阶段：“重要的叶子活动”（第一阶段）、“准混沌行为”（第二阶段）和“死亡”（第三阶段）。这项工作提出的理论模型结合了具有复杂指数共轭幂律的分形元素和具有时滞分支过程的分形元素。这种新颖的方法在复共轭幂律指数的虚部方面比先前提出的阻抗模型引入了额外的自由度。此外，它还提高了对复杂分支系统的行为变化进行精确建模的灵活性和多功能性，这些分支系统看似不确定的时间性质早先被认为是违反直觉和随机的。将分支过程结合到全面解释复杂的生物系统中，使我们能够更深入地了解可用频率尺度的中间范围内的电荷转移过程。此外，所提出的模型验证了自然发生的生物过程中具有复杂的指数共轭幂律的新分形元素的存在。 实验证实可以在解释复杂系统中的一类分支过程中发挥关键作用，并丰富现代分数阶微积分理论。