Fractal behavior accompanied by the complex-conjugated power-law exponents discovered in living systems: Analysis of the temporal evolution of impedance in silkworm cocoons

<p>In this paper, we continue using the theoretical model describing 3D-branching systems that is applied to describe the living system, such as the silkworm butterfly cocoons (Bombyx mori). The proposed fitting function that follows from the applied model allows us to describe completely with high accuracy (the fitting error is less than 0.1%) the whole stage of the temporal evolution of the silkworm cocoons in room conditions (during 13 days of the experiment the lowest temperature noted was 27 ℃ and the highest temperature was 29 ℃) and with relative humidity located in the interval [<em>H</em><sub>min</sub> 54% £ <em>H</em> £ 76% <em>H</em><sub>max</sub>] during 13 days (13 November 2023 to 25 November 2023) of the impedance measurements. The selection of this biological object is related to the fact that all possible conducting channels formed inside the given cocoon have 3D structures. Analysis of the measured impedance data shows that the measurements at the beginning of each day have a monotone character, while each measurement after the first measurement of each day has chaotic behavior. It means that during the night a cocoon “has a rest”. After this resting period, the applied voltage disturbs internal processes that are reflected in the behavior of the measured impedance. It has an oscillating character. These oscillations reflect the “regrouping” of conducting channels that take place inside the measured cocoon.</p>