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This particular example (with the bunnies and kitties) was formalized by Lotka-Volterra’s equations, and is THE prime example we teach students to illustrate how we can model an ecosystem.
Though the validity of this particular model in real life has been debated.
FYI it describes how each year, when hares multiply, lynx population also increases, until the pressure of predation from lynx is too much for hares and they begin disappearing, which in turns decreases lynx population, and the cycle begins anew the next year.