This cycle brings to mind the effect of cheaters in an established game-theoretic framework.

As example, in evolutionary game theory the mimic appears like the poisonous in order to reap the same benefits without bearing the cost of developing or cultivating a poison. This is frequency-dependent, and is limited by the number of cheaters. Once too many, the predators' odds of being poisoned by any one appearing insect begin to dwindle and the strategy loses effectiveness. This self-limiting feedback loop drives a sort of resonance in the numbers. Your intuition has grasped this same pattern, driven by the same mechanism, in the Bitcoin price.