I don't think it's a given that revolution and violence reset the cycle to liberalism. There would appear to be plenty of examples where the chaos just ushers in a greater degree of authoritarianism and how much liberalism that follows a power change is just caused by the period of new power consolidating its control?

Even if it's a matter of picking the right start and stop times to a cycle, every iteration would be heterogeneous enough that calling it a cycle is probably missing some important behaviors.