Fig. 1. Representation of the circadian rhythm. The plot on the upper denotes circadian process oscillation. the plot on the bottom denotes temperatur

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1 Biological autonomy and control of function in circadian cycle Chul-wook Park* International Institute for Applied Systems Analysis [Purpose] [Methods] [Results] [Conclusions] Key words:

2 Fig. 1. Representation of the circadian rhythm. The plot on the upper denotes circadian process oscillation. the plot on the bottom denotes temperature process oscillation between the circadian temperature (horizontal axis) and the body temperature (vertical axis).

4 Table 1. Experimental design 1 Condition Participants Normal 8 points 5:00 12:00 17:00 00:00 Trials at each circadian Task/rest (min) 6 1/5 cos cos

Fig. 2. Reflection of a potential function (HKB model).

unstable states (repellors), ϕ2 ϕ1 0 denotes a condition of nearly synchronized in-phase, and ϕ2 ϕ1 π (= 3.14, -3.14) indicates this in an anti-phase.

The movement speed denotes control parameter and the arrow indicates attractor. max max max max sin Fig. 3. Graphical representation of the data analysis 1.

5 Fig. 2. Reflection of a potential function (HKB model). The plot on the left denotes the intrinsic dynamics of the potential function [V(ϕ)], and the black balls symbolize stable states (attractors) and red balls correspond to unstable states (repellors), ϕ2 ϕ1 0 denotes a condition of nearly synchronized in-phase, and ϕ2 ϕ1 π (= 3.14, -3.14) indicates this in an anti-phase. The plot on the right represents the observed relative phase or phase relation between two oscillators at ϕ 0 deg (in-phase), or ϕ ± 3.14 deg (anti-phase = π). The movement speed denotes control parameter and the arrow indicates attractor. max max max max sin Fig. 3. Graphical representation of the data analysis 1. The plot on the left denotes the frequency range of the amplitude (horizontal axis = time series and vertical axis = displacement, with the upper figure denoting the left-hand side and the bottom denoting the right-hand side). The plot on the right illustrates the discrete relative phase synchrony (horizontal axis = time series, vertical axis = relative phase checked peaks).

6 Table 2. Experimental design 2 Condition Participants Normal 8 Abnormal (heat) 8 points 5:00 17:00 5:00 17:00 Trials at each circadian Task/rest (min) 6 1/5 6 1/5 Figure 4. Illustration of the temperature according to the experimental design. The horizontal axis denotes the temperature check time (TO = take off the ice/heat vest under the perturbation condition). The vertical axis is the level of the temperature change as normalized calculation. Table 3. Experimental design 3 Condition Participants Normal 8 Abnormal (ice) 8 points 5:00 17:00 5:00 17:00 Trials at each circadian Task/rest (min) 6 1/5 6 1/5 cos cos cos cos

7 cos cos π sin sin and and cos cos cos cos cos cos log log Fig. 5. Graphical representation of the data analysis 2 and 3. The plot on the left denotes the estimated entropy states (vertical axis) according to the time series (horizontal axis), corresponding entropy forces (plot on the right).

8 Table 4. Experimental result 1 5:00 12:00 17:00 00:00 P P P P P P P P T(C ) Figure 6. General tendencies in the normal condition. Normalized = standard score (Z calculation), blue line = fixed point shift, red line = variability as a function of the frequency competition, Temp = temperature (Celsius), 5:00, 12:00, 17:00, and 00:00. Table 5. Experimental result 2 N_5:00 N_17:00 Ab_5:00 Ab_17:00 N(I) AVER(H) STDEV(H) SES Table 6. Experimental result 3 N_5:00 N_17:00 Ab_5:00 Ab_17:00 N(I) AVER(H) STDEV(H) SES

Fig. 7. Entropy forces. The plot on the left denotes the entropy forces of the heat-based normal vs. abnormal conditions, which data was from the results 2.

9 Fig. 7. Entropy forces. The plot on the left denotes the entropy forces of the heat-based normal vs. abnormal conditions, which data was from the results 2. The plot on the right denotes the entropy forces of the ice-based normal vs. abnormal conditions, which data was from the results 3. Fig. 8. Illustration of the three-different experimental results. The contour (black ~ white) represents the 24 hour circadian process (T = temperature, H = entropy) as expressed by a sine function (pi/2 = 5:00, pi = 12:00, pi3/2 = 17:00, pi2 = 00:00) according to the optimized value of the system s state with arbitrary units of -1 to 1.

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