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University of Bath

Cumulative Innovation in Complex Social Systems

This research project seeks to uncover ways policy makers can stimulate socio-economic development and aims to deliver policy intervention evaluation tools.

Ariel view of Silicon Valley
Silicon Valley in the US is an iconic example of social and economic development based on self-reinforcing processes.

Dynamics of Cumulative Innovation in Complex Social Systems (DCICSS)

Social and economic development is often driven by self-reinforcing processes, which evolve within a geographical cluster. An iconic example of this is Silicon Valley in the US.

Using models of co-evolving systems to understand these social and economic dynamics, the DCICSS research project seeks to identify how policymakers can intervene to stimulate socio-economic development, and provide tools for evaluating policy interventions.

Our central questions are:

  • How can we conceptualise and model self-reinforcing processes of social and economic change?
  • How can we evaluate corresponding policy interventions?

We will address these questions by drawing on mathematical models of non-linear systems and apply them to a range of well-chosen empirical data sets, using carefully crafted statistical tools.

The project

Overview and outcomes:

  • Using mathematics to understand better co-evolving networked systems and innovation

  • Delivering a toolset for evaluating policy interventions and private initiatives

Modelling work

Jain and Krishna (2003) provided our theoretical starting point. They are interested in the dynamics of co-evolution and use network theory to explore autocatalytic sets (ACS) which are sets of simple molecular organisms that are unable to self-replicate, but each providing a catalyst for its fellows. Jain and Krishna use computational models to simulate such a dynamic system. This reveals ‘punctuated equilibria’, with processes of growth and then partial collapse.

The Jain and Krishna model embodies two timescales. The fast (or short) dynamics correspond to fitness propagation within the network; the slow (or long) dynamics correspond to the update and reconfiguration of the network. These features can be interpreted as local innovation (transfer of knowledge between similar technologies) and global innovation (updates to the global technology system).

We apply this model to the study of self-reinforcing processes of social and economic change.

The Jain and Krishna model has attracted a good amount of attention in the literature on complex network dynamics. Nevertheless this is the first and most ambitious attempt to apply their model on a multi-disciplinary basis and with a strong empirical and policy emphasis.

Empirical case studies

Patents: The initial empirical case study is on patents, and we have been given access to the PATSTAT datasets we require. Using the case study of patents as our template, we will extend the research across further social and economic case studies with a view to expanding the mathematical, statistical and empirical scope of the Jain and Krishna model.

Additional case studies are likely to include some of the following:

  • Mergers and Acquisitions to track the development and co-evolution of different capabilities in firms
  • Financial system to model the co-evolution of risks within connected financial systems
  • Welfare regimes to model how institutions concerned with social security, vocational training, employment, etc. co-evolve to produce a number of distinct regimes typical of particular countries
  • Developing countries to link science and engineering innovations with the institutional contexts and ‘soft technologies’ of the developing world
  • Digital social networks to examine the dynamics of social media, and the insights offered by our modelling for data analytics and digital governance

Research overview, data and papers

We are pleased to make available our research data and first findings on co-evolving systems, technology networks, and innovation patterns.

Project team

This research is led by a multi-disciplinary team of mathematicians and social scientists at the University:

External research associates

  • Dr Emanuele Pugliese, Fellow at the Institute for Complex Systems, National Research Council (Italy)
  • Dr Lorenzo Napolitano, post-doctoral Fellow, Institute for Complex Systems, National Research Council (Italy).

Other colleagues will join the research team as new empirical case studies are undertaken.


We gratefully acknowledge the assistance of PATSTAT at the European Patent Office, who kindly supplied the datasets we are using for our patent case study.