An introduction

What makes a system complex

A system is a group of interconnected elements. It becomes complex when its behaviour is determined by the interactions between those elements rather than in the elements themselves — when it's the connections, not the parts, that decide how the system behaves.

That is the difference between a complex and a complicated system. A complicated system - a calculator, an engine, a legal text - can have many intricate parts, but you can take it apart and understand it piece by piece to reconstruct the whole. In a complex system, this is impossible because the whole is also defined by how the parts interact.

Each element may follow simple local rules, with no single entity in control, and produce new, sophisticated collective behaviour or properties that none of them possesses on its own.

Why study Complex Systems

Complex systems are all around us, and many go unrecognized as complex for a long time. The reason is that when a complex system is near equilibrium, it can be locally approximated by a simple one, and the rules we derive for it will continue to hold until the system drifts from that equilibrium. Epidemics, markets, ecosystems, cities, traffic, and the human mind are all complex systems that can be understood through the same small set of ideas. And the science of complex systems provides a conceptual framework that allows us to study these systems across disciplines.