And mimicking heart rate and breathing patterns is very real. A few weeks ago, my son was having some respiratory issues. (It happens periodically.) I was nervous overnight, and after continually getting out of bed to check his distressed coughs, I decided to just lay with him to monitor his breathing.
As I started to fall asleep next to him, I felt short of breath. At first, in my sleepy haze, I panicked thinking there was something in his room, in the air, that was causing it, but then I realized that I was so focused on his breathing, that my body was actually mimicking his breathing patterns! I was kind of hoping for the reverse effect, but it was pretty amazing, nonetheless.
These studies that prove human nature-- though not surprising-- are fascinating to me.
http://www.psychologytoday.com/blog/the-athletes-way/201304/the-neuroscience-calming-baby