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) = 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.

The scaling relationship between citation‐based performance and coauthorship patterns in natural sciences

“…This result supports hypothesis 1. A power law with an exponential cutoff is a degenerate form of a power law (Katz, ). A pure power law is scale‐invariant from x min to the end of the distribution; however, a power law with exponential cutoff is only scale‐invariant from x min to the point at the far right‐hand side of the distribution where the exponential decay begins to dominate the power law.…”

Allometric scaling in scientific fields

“…However, scaling laws are different from the recent interest in power laws, which generally describe probability distributions P (x) ∼ x −α , e.g. the distribution of citations [3,32]. In power laws, due to the fact that to be a normalizable probability distribution function the power law usually holds only at the tail part of the distribution function and also due to noises in rare events at the very end of the tail part so that sometimes a cut-off has to be introduced, the exponents can be better estimated by the maximum likelihood method [33][34][35] than OLS regression.…”

“…in scientific fields, and furthermore, whether and how such a relation can be used to indicate developmental stages of scientific fields? This question attracted considerable attention [1][2][3][4]. In general, scaling laws are helpful to answer the above questions.…”

“…In this study, we present a scaling analysis between size, which is measured by the number of authors, and input/output, where the former is represented by the number of references and the latter refers to number of papers and of received citations, of subfields at various levels. In a sense, we treat subfields as the universities, cities and countries in previous studies [1][2][3][4].The formation, flourishing and decline of scientific fields, like the formation, rise and fall of cities, countries and industrial sectors [5,6], certainly comprise a question worth studying, although of a more abstract nature since the boundaries between scientific fields are less well defined than those of, e.g., cities. Several researchers have begun to study the dynamic evolution of scientific fields [7,8] or to evaluate the scientific performances of universities [9, 10], research groups [11-13] and metropolitan areas [14].We note that in studies of cities, countries and many other systems, analyses of the scaling between their outputs/inputs and their sizes play an important and unique role.…”

“…In this study, we present a scaling analysis between size, which is measured by the number of authors, and input/output, where the former is represented by the number of references and the latter refers to number of papers and of received citations, of subfields at various levels. In a sense, we treat subfields as the universities, cities and countries in previous studies [1][2][3][4].…”