Thoughts: Child development and humanity

From what I've read about the development of children who have been terribly abused or molested, it is very common for those same victims to go on to become the perpetrators of the same form of torture which they, themselves, endured.
I wonder if it is possible that the course of populations of people would fallow a similar trajectory. If we take Chaos Mathematical theory about the weather, for instance. The MIT mapping computers tell us that the weather is governed by a very complicated mathematical equation based on recursion. This is called the "Lorenz Attractor," and can be acuratly depicted as a fractel. If we accept that nature is based on this constant recursion of elements, (a fair Middle-Level bridging theory in Anthroplogy, based on the low-level evidence of Chaos Theory): Then why wouldn't human populations be based on a similar form of repetetive recursion, biologically and historically. In other words the seeming chaos of the rise and falls of human societies could similarly be governed by mathematical factors. This is hard to conceive of, with free will and all, but never-the-less it is scientifically sound ( combined with Quantum Physics one still has free-will, without any mathematical paradox).
I started thinking about all this in relation to Israel. One the one hand they were a terribly abuse people. On that same hand, they are now (speaking of the policies of the government) a terribly abusive people. Taken in consideration with the information about child psychology, it should be evident what has ocured. This also brings me to Carl Jung's theory of the Collective Unconscious, possibly being the creation of this . And besides Israel, we can look at the same recursion on a Larger Historical PErspective. Seeing the USA as a further loop in what was once ancient rome, etc...