# Systems Theory/Order-Chaos
## Order and Chaos

Systems exhibit behaviors. These behaviors are the result of the application of parameters for the system’s elements - the rules. The subsequent behavior is interpreted based on the knowledge of the current system and the anticipated results of various inputs and processes. When systems behave in the expected manner they are generally regarded as stable and thus, in order. The term “order” is not absolute, however. Generally, terms such as “stable”, “balanced” and “in order” are describing all known (considered) inputs and outputs of a system, and based on those factors alone, the system appears to be exhibiting the desired behaviors.
Order describes the history of a system or system segment. Order illustrates that a system has responded to a rule or rules that have made the system behave in a manner that is expected. Specific forms of order exist in many systems: homeostasis, autonomy and chaos. These forms of order describe the system’s inherent behavior and how fluctuations in a system can occur.
Homeostasis
When systems respond to external forces by eventually returning to their starting points, they are considered homeostatic. An example of this form of order is in living systems. A population of animals supported by an island will, over time, maintain a certain number. An external disease, predator, or other force may diminish the number, but eventually the population will increase (all other forces being equal). If the population spikes, shortages in food will eventually lead to less animals. These natural laws work to create homeostatic order. Systems do not require external forces to create fluctuations, though. Often, systems that maintain the same inputs and processes over time experience diminishing desired outputs due to entropy (see wikipedia:Entropy).
Autonomy
Systems that produce ongoing fluctuations or change but follow an average output yield autonomy. Autonomy is best described as oscillation in a system over a period of time. Although this oscillation is not necessarily harmonic motion, it does tend to be around a general mean. A small change in the input parameters of homeostatic order can create autonomic order.
Chaos
If the system fluctuates further it can become unpredictable. Although this does not indicate system failure, the behavior suggests “deterministic unpredictability” – the concept that the same inputs generate different results. This unpredictability is often considered chaotic. The term “chaos” does not mean that the system is failing or will fail; rather it is a method of describing a system that can not be predicted will full certainty. Most often, systems are considered to be chaotic when the underlying rules are unknown, thus the results can not be known. This, however, does not mean that unpredictable or complex output structured systems are chaotic. When there is no underlying rule that governs the unpredictable system it is considered to be non-deterministic.
An example of a non-deterministic system is a coin flip. Although the coin has only two sides, predicting which side will land face-up is quite difficult. There is no underlying rule that governs the coin flip; rather it is the interaction of several inputs: the force of the flip, the original position, friction of fingernails, wind speed and direction, height of the flip, rotational velocity, current gravity of the object on which the person is standing, etc. Unpredictability results from not being able to consider all of these factors. Although we may assume that after many flips the number of times each side lands face-up will be equal, it is not a definite prediction. This system is not considered autonomic since it does not internally correct itself, nor does the low number of outputs available immediately make it a homeostatic environment.
Thus, chaotic systems can be considered to have a highly complex order, sometimes too complex to understand without the aid of analytical tools or complex mathematics. Most approaches to studying complex and chaotic systems involve understanding graphical plots of fractal nature, and bifurcation diagrams. These models illustrate very complex recurrences of outputs directly related to inputs. Hence, complex order occurs from chaotic systems.

## References

* Serendip. On Beyond Newton: From Simple Rules to Stability, Fluctuation, and Chaos
http://serendip.brynmawr.edu/complexity/newton
* Cybernetics:Principles of Systems and cybernetics: an evolutionary perspective
http://intelegen.com/genius/systems_and_cybernetics.htm#Cybernetics%20The%20Principle%20of%20Autocatalytic%20Growth
* Sterman, John. Business Dynamics: Systems Thinking and Modeling for a Complex World. 2000.