The point of "Complex Dynamic Systems" or "Chaos Theory" is that the more parts that are interacting, the more unpredictable the outcome will be. If they were ONLY the sum of their parts, the predictability would be easy.
Good point from Michael. An area that I am interested in is 'wickedness' / complexity in health promotion. The term wicked refers to the fact that they are devilishly complex systems - especially around policy. You can't gather all the policy together and then squeeze them into one overarching policy - so there is no single solution that can be the sum of all parts.
There are several examples we might use to explain how complex systems are not necessarily the sum of their components. A good example is biological complex systems such as the central nervous system, or the biological process in the liver, and the digestive system. Careful assessment of biological processes and outcomes of functions are far many. However, the complexity of the system at the molecular and cellular level and the integration across systems are behind such observation. Read for example the attached article
Complex systems are creating processes called self-organization, emergence, self-assembly, self-repair/healing, and many other apparently quite complex interactions.
In complex systems are present entities/agents that mutually interact locally using some kind of function describing their change according to their environment. In general, complex systems are unpredictable. We have no theories describing them. It is necessary to simulate them.
Complex systems are very difficult to describe theoretically and to apply them to real observed natural phenomena. An explanation from the beginning of how this works can be found in many of my publications and open software. Just three major publications that explain it and one software follow (the poster takes only five minutes to read, 2nd item in the list).
One can become easily lost in the number of publications dealing with this exciting subject. That is why those recommended sources help you to penetrate to the core of the knowledge quickly.
Enjoy complex systems. They are fascinating and they have a great future. :-)