It probably is related to laplace transforms... Pretty much anything oscillating can be analyzed with a laplace transform.
I'd guess in your case it's because each LED has it's own constant current power supply, and when the battery voltage gets low, the power supply becomes unstable, but the exact flicker rate depends on small variations in the components it's made from.
I'd guess in your case it's because each LED has it's own constant current power supply, and when the battery voltage gets low, the power supply becomes unstable, but the exact flicker rate depends on small variations in the components it's made from.