...states that a system under stress will tend to change in such a way as to minimize the effects of that stress.

The butterfly effect tells us a tiny change now can result in enormous consequences later. But there is another effect that tends to counter this. Many changes have results that tend to damp out, that is, a change now will cause future changes, that tend to progressively minimize until equilibrium is reached further on down the line. Jump in a flat pool and you create waves; wait long enough and the pool becomes flat and smooth again. Perhaps the water temperature will be slightly higher, but that change will be uniformly distributed, spread out so its effects are negligible.

A major asteroid strike may wipe out the dinosaurs and totally disrupt global climate, but a meteorite hit that takes out only one dinosaur may have no long lasting effect at all, except to the dinosaur and his immediate surroundings.

Complex systems have the ability to absorb perturbations and then "relax" back into a state of equilibrium, and the induced changes diminish over time, not continue increasing over time. This effect depends on the nature of the affected system, the nature of the perturbing effect, and the period of time you are considering. Put in its simplest form: tap a cone resting on its base. A small tap causes it to tilt over, but eventually, counteracting forces cause it to fall back onto its base again as before. It recovers. But if you strike the cone hard enough, it will tip over and never recover it's original position. If you jump into a pool hard enough, with enough weight, the water splashes out and you never go back to a state of smooth water. Complex systems can absorb change and recover, but they also can experience so much change that they exceed their ability to return to a ground state. You can bend a stick and it springs back to its original shape. If you bend it far enough, it breaks.

Our common everyday experience (and the laws of thermodynamics)tells us this is the case. Both effects occur simultaneously, and operate at different scales of time, space, energy and complexity. A Jurassic butterfly won't necessarily cause a hurricane tomorrow, but everything that happened in the Jurassic plays a role in what is happening right now.

I once read a science fiction story where these counteracting effects were a property of space-time itself. If small events lead to big consequences, time is "curved" negatively. If they tend to damp out and return to equilibrium, then time is curved positively. We know that both these curvatures simultaneously exist, depending on the scale in space and time you are considering. But what is the overall curvature, summed up over all space and all time?

At one time, (about 50 years ago) there was some controversy about this. Most scientists tended to believe the universe was essentially static and unchanging: the steady-state theory. Oh sure, things were very busy, but if you looked at a large enough area over a long enough time, the distribution of matter and energy and the organization of the galaxies and the proportions of the elements would always be about the same. Today, science tends to believe the universe is evolving. It had a beginning, it has morphed into its present configuration, and it will eventually disperse into a thin soup of near-vacuum and radiation at constant temperature. Big Bang, cosmos, and heat death. I.e., it will go from singularity, to infinity, to nothingness; birth, life, oblivion. Sort of like us.