Have you ever tried to connect a charged cap to a digital (say, CMOS-inverter-based) oscillator as its load, and let it be discharged? If not, you might be surprised that the voltage on the cap changes not according to exponential but rather hyperbolic curve. There are also interesting interconnection laws on these voltage-dependant resistors. More about it can be found in http://onlinelibrary.wiley.com/doi/10.1002/cta.2010/full
I am looking for other physical phenomena with similar characteristics.
Hm, it's stated here
https://blog.kissmetrics.com/hyperbolic-discounting/
that "The brain uses hyperbolic discounting as a learning mechanism"
However, this article
http://www.intmath.com/blog/mathematics/hyperbolic-and-exponential-discounting-10115
advices "Next time some salesperson is pressuring you to buy something right now, ask him about the difference between exponential and hyperbolic discounting."
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