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.

我们提出了一个数学模型，以粗略的定性来近似学术界中近亲游说与学科间的相互作用，并执行一参数和二参数数值分叉分析以分析其动力学。学科多样性是发展跨学科性的必要条件，今天，跨学科性已被认为是建立一个充满活力的学术环境的关键，该环境具有更大的研究和技术突破/创新潜力。但是，包括制度政策和行为态度在内的若干因素的相互作用为推进跨学科性设置了重大障碍。“学术僵化”可能会因积极的学术游说行为而有利于近亲繁殖。该模型由四个耦合的非线性常微分方程组成，它们模拟了某些类型的学术行为和与学科多样性水平有关的知识进步率之间的相互作用。还研究了控制策略抑制近亲繁殖的效果。数值分叉分析显示出丰富的非线性行为，包括多重稳定性，持续振荡，极限环的极限点，同斜分叉以及余维两个分叉，尤其是Bogdanov-Takens和Bautin分叉。