not that simple, rising prices drive the searches, but more searches generates more articles and gives more exposure which adds new adopters and drives the prices up
it is some sort of closed loop exponential feeding law, when the black hole collapses, it looks like the same occurs but in reverse
how long between two cycles? 100% psychological: until people forget and journalists/bloggers think it's time to make an article about bitcoin again because people forgot about it
how do more searches 'generate' more articles?