There are four main characteristics of Chaos Theory that I found applicable so fr for management systems and organizations. Storage Attractors (AKA Butterfly effect), Universality, Fractals, and Bifurcations.
I believe that strange attractors are the most common attribute of chaos systems. There is so much noise around it, so I’ll focus just on the following three characteristics. If I see any comment that requests elaboration on strange attractors, I’ll be happy to post about it as well.
Universalities are common rules of order that make chaos. Sound paradoxical, that’s real life. Chaos starts with fix attractors, moves into periodic attractors, than to chaos attractors and finally switch between periodic and chaotic attractors. That’s right chaos start from deterministic (fix attractors). The rate of change between those steps is more or less fixed number 4.66. Universality also found in the distribution between order and chaos. No matter what chaos system will be examined, the graph depicts the distribution will look the same.
Understanding Universalities help to understand how order turn into chaos and what are the indications that chaos is taking place. Chaos is not necessarily negative. You can take advantage of it to reinforce a positive trend and changes in the organization. I saw more than once that the rules that turn order into chase can be reversed to turn chaos to order.
Personally, I believe that an organization that finds how to switch between order and chaos generates a lot of energy to be far away from equilibrium and to be very creative.
Fractals: Fractals are simple structures that by following simple rules create complex systems. Fractals are all around us! Snow flecks, trees, and leaves are a few examples.

Organizations are fractals as well, not hierarchies. Well, they are hierarchies because someone creates them as hierarchies, but people are grouping in social systems following fractals and organization are first of all fractals! If we add to the containing structure of fractals ranks and authority, we will end with hierarchies. But we don’t have to. Organizations can operate as fractals, the same way our brain works!
If you learn fractals, you’ll find out that the containing elements are there to serve and support the contained elements; not to command, control or tell them what to do. That is the way that very successful organizations for a long time are working. By the way, the market or cities are good examples.
Bifurcations, in a nutshell, is a pattern that describes how a system changing from a phase of stability, through minimizing stability and increasing instability until a sudden change that happened due to no stability. In each step, the system can create a new structure or behavior. A good example is the changing of water to ice.
Bifurcations create tipping points, which are a big jump in the system when the ratio between elements in the system reaches 0.5. Bifurcations are one of the main reason why creating random interaction between people in the working place may have a significant impact on group performance.
Understanding Bifurcations paved the way to utilize chaos and harness it to the benefit of your organization.