Definitions

Complex system: A system of interconnected simple parts that together exhibit a high degree of computational complexity from which emerges a higher order behavior (source: wikipedia [1]; see also wikipedia entry on "complexity" [2])
Emergence: "emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems." (source: wikipedia [3])
Non-linearity: ...