Aquatic species of Utricularia are carnivorous plants living in environments poor in nutrients. Their trapping mechanism has fascinated generations of scientists and is still debated today. It was reported recently that Utricularia traps can fire spontaneously. We show here that these spontaneous firings follow an unexpected diversity of temporal patterns, from "metronomic" traps which fire at fixed time intervals to "random" patterns, displaying more scattered firing times. Some "bursting" traps even combine both aspects, with groups of fast regular firings separated by a variable amount of time. We propose a physical model to understand these very particular behaviors, showing that a trap of Utricularia accomplishes mechanical oscillations, based on continuous pumping and sudden opening of the trap door (buckling). We isolate the key parameters governing these oscillations and discuss the effect of their fluctuations.