if predators breed annually, that means that one year is the clock-tick, not the cycle. as a very simplified example, let's say there is some fixed availability

if predators breed annually, that means that one year is the clock-tick, not the cycle. as a very simplified example, let's say there is some fixed availability of prey. so if there are a ton of predators born and/or come to maturity in one year, they will exhaust the food supply, spend their time and energy fighting for food or starving, and have a population crash next year. the reduced population that year will have a glut of food and a surplus of time and energy for breeding, leading to a boom the year after that, for a two-year cycle with a one-year tick.