What is a Complex Innovation System?

Innovation systems are frequently 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) = kxa where the exponent, a, is a measure of the scale-invariance. The purpose of this paper is to describe and illustrate that innovation systems have properties of a complex adaptive system and in particular scale-invariant emergent properties indicative of their complex nature. These properties 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. And citations or references to these articles are an indirect measure of the impact the knowledge has on the research community. These measures are used to illustrate how scale-invariant properties can be identified and quantified. Peer-reviewed papers indexed in Scopus and in the Web of Science were used as the data sources to produce measures of sizes and impact. Papers indexed in Scopus were classified into fields using the Scopus, NSF and MAPS schemes. The evolution of the overall and field level impact distributions were examined to see if they had a reasonable likelihood of being scale-invariant as they aged. Also, correlations between impact and size were explored to see if they were scale-invariant too. The findings show 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. Scale-invariant correlations are shown to exist between the evolution of impact and size with time and between field impact and sizes at points in time. However, it was found that care must be exercised making these measures as the method of classification may hide emerging properties. The confirmation that an innovation has common characteristics of an adaptive complex system and scale-invariant emergent properties allows us to confidently say that the global research system has a reasonable likelihood of being a complex innovation system. And using the recursive nature of scale-invariance it is reasonable to assume that regional, national, local and sectoral level systems contained within it are complex with scale- invariant properties too. Measures and models based on the scale-invariant properties of complex innovation systems can provide new and novel insights about an innovation system useful for informing public policy.