Organisations, Innovation and Complexity: New Perspectives on the Knowledge Economy

University of Manchester
9-10th September 2004

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Complexity in Discrete Innovation Systems

Masaaki Hirooka

Institute of Technoecomics
Kyoto, Japan

Abstract

The innovation process is a kind of discrete system, and knowledge transfer from person to person is a decisive element in this system. This paper discloses the nature of the complexity in innovation systems.

We have examined the innovation process and found that an innovation system consists of three phases. That is, the innovation paradigm can be described using three logistic curves in which the first phase is the development period of core technologies starting from an epoch-making discovery or a key invention, the second phase is a locus of developments of a series of new products, and the third phase is the diffusion of innovation products forming a new market. These three loci are termed the technology trajectory, the development trajectory, and the diffusion trajectory, respectively. While it has been well known that the diffusion of innovation products obeys a logistic equation, as first shown by Griliches in 1957, we have found that the other two trajectories are also described by logistic equations. The fact that these loci obey logistic equations means that each trajectory becomes mature within a definite time span. This nonlinear nature exhibits various interesting characteristics. In particular, the development trajectory clearly indicates the timing for innovation commitment.

In the case of the electronics paradigm, the technology trajectory comprises the history of core technology developments starting with the discovery of the transistor by Shockley et al., and the development trajectory is composed of the development history of semiconductor chips. As described by Moore’s law, the degree of integration of semiconductor chips quadruples every three or four years. This means that the development trajectory is composed of a series of small fractals of each stage of development. Various industries adopt IC chips to develop new products, and the locus of this development history creates fusion trajectories along the electronics development trajectory itself. These fusion trajectories form a bundle along the development trajectory of electronics. This is a bundle fractal. Information technologies are formed by three innovation paradigms: computer, IC, and multimedia. On each development trajectory, there have been developed various systems and software packages. Along the development trajectory of electronics are, for example, NC (numerically controlled) machine tools, FMS (flexible manufacturing systems), POS (point of sales) systems, CALS (computer-aided logistic systems), and EDI (electronic data interchange) systems. The development of these systems forms a series of small fractals along the development trajectory of electronics. In the case of the high polymer industry, the development trajectory is composed of bundle and series fractals of various unit products. While an innovation paradigm is established with an explicit discipline, various fractals are involved inside the paradigm, as described above.

As shown in previous papers, diffusions of various innovations gather and form a cluster on the upswing of Kondratiev cycles. This cluster formation is interpreted as a kind of self-organization. The phenomenon that fusion trajectories formed by various existing industries gather along the development trajectory of innovation itself and create a bundle fractal is also ascribed to a self-organization mechanism.

The discrete system of innovation is discussed in terms of a logistic difference equation instead of a differential one, and the complexity of innovation systems is interpreted.

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