I was in a crowded parking garage the other day. A car alarm went off. And that made other car alarms go off. And so on. When I left there were about 5 alarms going off.
I came back 10 minutes later and they had all stopped.
what stops this type of chain reaction from going on forever?
Differing levels of sensitivity to set the alarms to turn on than to turn them off. In other words, a bump or nudge of X to turn them ON but 2X to keep them on. If they weren’t designed something like this, none would ever turn off.
That would be a good example to teach how waves propagate to science students.
BTW, is this sort of chain reaction common? Obviously it requires pretty sensitive car alarms for one to set another one off. It’s a good thing we don’t have earthquakes here…
OK, I understand you when you say they need a bigger vibration to keep going. But I picture the the chain reaction propagating (yes, much like a wave) round and round, so each car goes off for a minute or two, setting the next one off, more or less in a circle. The wave of noisy cars would go round and round the garage for ever and ever. 
Is there something to stop that?
I think it is a bit uneven and unreliable to be an ideal wave propagation example. Cars stopped at a stop light are another wavefront example. E.g., if each car tries to keep 3 seconds between its front and the car ahead of its rear, that means there is roughly a 3 second delay before each car starts. So motion start is like a wave propagating backwards from the light. People who honk as soon as the light goes green because the many cars in front of them haven’t all started moving at once must think cars at a light are like a train, so they can all start with little delay between them. OTOH, I admit that isn’t a perfect example either, because people delay different times, and cars are of different lengths.
I already explained that there is…
The battery.… 
And what Mustangman said…
I used to drive my hot rod around parking lots back in the 90’s setting off car alarms from the exhaust on my car… lol
Mustangman, you didn’t get my point.
It would seem possible for the alarm to shut off, then turn on again when the wave of noise and vibration wound around to its portion of the garage again.
Unless going off tends to suppress going off again for maybe 10 minutes… Is that what you mean? Which would be a bad thing that a thief could take advantage of. And might not be long enough for a really big garage.
Are you sure the alarms weren’t triggered by a vehicle’s exhaust system? Aftermarket alarm systems have impact sensor that can be sensitive to the deep vibrations from a loud exhaust system, the alarms usually time-out after 60 to 90 seconds. One car would need to be parked close to the other to have the alarm triggered by a horn or siren.
My opinion it was more likely someone going around checking for open doors to steal stuff inside than a car alarm setting off an adjacent car.
In this particular case, the cars whose alarms went off were scattered about the parking garage.
But that’s interesting.
I do recall several alarms on my street going off after someone drove by playing loud music…