The Detection of Self-Similar/Branching Processes in Complex Biological Systems: Analysis of the Temporal Evolution of Impedance Measurements in Tulsi (Holy Basil) Leaves “Ocimumtenuiflorum”

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.