Complexity and chaos are being invoked with
increasing frequency with some looseness in how they have
been translated from their origins in mathematics and physics,
which is leading to confusion and error in their application.
Nonetheless, used carefully, ‘‘complexity science’’ has the
potential to invigorate many disciplines and may
lead to important practical outcomes. pdf 
System is simply the name given to an object studied in some field and might be abstract or concrete; elementary or composite; linear or nonlinear; simple or complicated; complex or chaotic.
Complex systems are highly composite ones, built up from very large numbers of mutually interacting subunits (that are often composites themselves) whose repeated interactions result in rich, collective behaviour that feeds back into the behaviour of the individual parts.
Chaotic systems can have very few interacting subunits, but they interact in such a way as to produce very intricate dynamics.
Simple systems have very few parts that behave according to very simple laws.
Complicated systems can have very many parts too, but they play specific functional roles and are guided by very simple rules.
Some systems have a property known as criticality. A system is critical if its state changes dramatically given some small input. To make sense of this, we need to introduce several new concepts.
An order parameter is a macroscopic (global or systemic) feature of the system that tells one how the parts of the system are competing or cooperating with one another.
The control parameter is an external input to the system that can be varied so as to change the order parameter and so the macroscopic features of the system.
The general study of such behaviour is the theory of critical phenomena.
Scaling laws, or power laws have the following form: f(x) , x 2a in other words, the probability f(x) of an event of magnitude x occurring is inversely proportional to x.
If a system displays power law behaviour then it is scale-free and its parts have scale-invariant correlations between them. What A simple guide to chaos and complexity this means is that the system does not possess a characteristic scale in the sense that events of all magnitudes can occur.
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Complex Systems: Science for the 21st Century. A U.S. Department of Energy, Office of Science Workshop. pdf