What Is a Complex Innovation System?

Abstract

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) = kxα, 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.

Measuring synergy within a Triple Helix innovation system using game theory: cases of some developed and emerging countries

“…with more than two variables. Innovation systems are complex systems (Katz 2006(Katz , 2016; Leydesdorff (2003) asserted that the Triple Helix of university-industry-government relationships constitute a complex system that, therefore, could be analysed with techniques and tools from cybernetics, information theory, game theory, decision theory, topology or mathematics of relations or factorial analysis (von Bertalanffy 1973). Recently, Mêgnigbêto (Mêgnigbêto 2017;2018) proved that the Triple Helix innovation system with publication as unit of analysis is a cooperative game with transferable utility; then, the core, the Shapley value and the nucleolus were proposed as indicators of synergy.…”

The scale-invariant properties of the citation-based performance of internationally co-authored articles

“…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 in the form, ( ) = where the exponent, , is a measure of the system's scale invariance (Katz 2016). The global research system is an example of a complex innovation system (Katz 2016).…”

“…A scale invariant property can be identified because it is solely described by a power law function in the form, ( ) = where the exponent, , is a measure of the system's scale invariance (Katz 2016). The global research system is an example of a complex innovation system (Katz 2016). Peerreviewed publications containing knowledge in specific areas are a characteristic output of such a system.…”

“…The number of citations to these articles is an indirect measure of the impact the knowledge contained in these publications has on the research community. Received citations are used to illustrate how scale invariant properties can be identified and quantified (Katz 2016).…”

“…As this process gets larger, a complex network emerges. This network is composed of a large number of interconnected nodes whose connectivity (node degree) has a power law probability distribution characterized by ( ) = − for ≥ 1 (Katz 2016;Newman 2004). The exponent, , called the scaling factor, and are constants for a given network.…”