Mathematical modelling and numerical bifurcation analysis of inbreeding and interdisciplinarity dynamics in academia

We address a mathematical model to approximate in a coarse qualitative the interaction between inbreeding-lobbying and interdisciplinarity in academia and perform a one and two-parameter numerical bifurcation analysis to analyse its dynamics. Disciplinary diversity is a necessary condition for the development of interdisciplinarity, which is being recognized today as the key to establish a vibrant academic environment with bigger potential for breakthroughs/innovation in research and technology. However, the interaction of several factors including institutional policies, and behavioural attitudes put significant barriers on advancing interdisciplinarity. A “cognitive rigidity” may rise due to reactive academic lobby behaviours favouring inbreeding. The proposed model consists of four coupled non-linear Ordinary Differential Equations simulating the interaction between certain types of academic behaviour and the rate of knowledge advancement which is related to the level of disciplinary diversity. The effect of a control policy that inhibits inbreeding-lobbying is also investigated. The numerical bifurcation analysis reveals a rich nonlinear behaviour including multistability, sustained oscillations, limit points of limit cycles, homoclinic bifurcations as well as codimension-two bifurcations and in particular Bogdanov–Takens and Bautin bifurcations.