Path dependence in an evolving system: a modeling perspective

In recent years, path dependence has gained increasing scientific attention in many disciplines, leading to various new concepts and notations, such as path creation or path plasticity. However, if mathematical arguments are used, they are based on the early works by Brian W. Arthur and Paul A. David, usually referring to the mathematical concept of ergodicity. We extend their mathematical framework and develop a graphical representation of systems that allows for a metaphorical discussion of system behaviors beyond the original cases, especially in evolving systems, and the inclusion of the recently developed concepts within path dependence. Visualizations are used to explain the definition and characteristics of seven types of path dependence: lock-in, path-breaking, path-furrowing, path plasticity, path formation, path creation, and path selection. Although these visualizations are explained verbally and can be understood without a mathematical expertise, a mathematical model is used to generate them. The deduction of the metaphorical concept from a mathematical model guarantees the completeness of the identified processes and the rigor in their categorization as well as the identification of respective characteristics for their distinction. However, the aim of the paper is to provide an illustrative concept that allows researchers to classify and structure the various path-dependent processes they observe in their application. While five of the identified processes are in line with concepts from the literature and are defined accordingly, we also detect a sixth process that is new to the literature so far: path-furrowing. Moreover, slightly deviating from the literature, we define path selection as the possibility to choose a path intentionally, thereby focusing on the mindful choice of options.