Innovation systems are sometimes referred to as complex systems, something that is intuitively understood but poorly defined. A complex system dynamically evolves in non-linear ways giving it unique properties that distinguish it from other systems. In particular, a common signature of complex systems is scale-invariant emergent properties. A scale-invariant property can be identified because it is solely described by a power law function, f(x) = kx α , where the exponent, α, is a measure of scale-invariance. The focus of this paper is to describe and illustrate that innovation systems have properties of a complex adaptive system. In particular scale-invariant emergent properties indicative of their complex nature that can be quantified and used to inform public policy. The global research system is an example of an innovation system. Peer-reviewed publications containing knowledge are a characteristic output. Citations or references to these articles are an indirect measure of the impact the knowledge has on the research community. Peer-reviewed papers indexed in Scopus and in the Web of Science were used as data sources to produce measures of sizes and impact. These measures are used to illustrate how scale-invariant properties can be identified and quantified. It is demonstrated that the distribution of impact has a reasonable likelihood of being scale-invariant with scaling exponents that tended toward a value of less than 3.0 with the passage of time and decreasing group sizes. Scale-invariant correlations are shown between the evolution of impact and size with time and between field impact and sizes at points in time. The recursive or self-similar nature of scale-invariance suggests that any smaller innovation system within the global research system is likely to be complex with scale-invariant properties too.