Use of logistic regression

How do I use logistic regression with “cyclical” time data?

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I want to use logistic regression to estimate the probability of whether an organism is active or not. My independent variable is time of day and my dependent variable is binary (1 = active, 0 = not active)

While time is continuous, in this case it loops back into itself. After 24 hours (or 1440 minutes) the t-variable resets to zero. This would mean that the graph would have to travel upwards and then back down into itself. I also suspect that the curvature upwards may be different from the curvature downwards.

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