The dynamics of functioning investigating societal transitions with partial differential equations

In this article a mathematical framework is introduced and explored for the study of processes in societal transitions. A transition is conceptualised as a fundamental shift in the functioning of a societal system. The framework views functioning as a real-valued field defined upon a real variable. The initial status quo prior to a transition is captured in a field called the regime and the alternative that possibly takes over is represented in a field called a niche. Think for example of a transition in an energy supply system, where the regime could be centrally produced, fossil fuel based energy supply and a niche decentralised renewable energy production. The article then proceeds to translate theoretical notions on the interactions and dynamics of regimes and niches from transition literature into the language of this framework. This is subsequently elaborated in some simple models and studied analytically or by means of computer simulation.