Yes, there are tipping points. Any system has them. That said, just because any system has tipping points does not mean that those systems are by nature fragile. Big, complex systems as our biosphere is one have tipping points that will produce certain consequences that will then only affect a tiny portion of that entire system. Most of the time with little or no consequence to the whole. Our biosphere is neither perfect nor balanced or fragile. The swelling of our sun will doubtlessly kill it but short of that, what some ants do in it is of little consequence.
When a threshold is crossed the physical system responds with positive and negative feedbacks until settling into a new climate state as the perturbation damps out.