Lotka–Volterra Predator & PreyRabbits breed; foxes eat rabbits and starve without them. Plot foxes against rabbits and the story becomes a loop the system circles forever: rabbits boom, foxes follow, rabbits crash, foxes crash, rabbits recover.Alfred Lotka (1925) and Vito Volterra (1926, explaining a spike in Adriatic sharks) wrote two coupled equations. They have no friction term, so every starting mix rides its own closed orbit — the populations never settle, they oscillate a quarter-cycle out of step.