Intrinsic risks of managing multiple enterprises: a simple deterministic model highlighting unstable patterns

In this paper, we present a simplified mathematical model using a system of ordinary differential equations to describe the relationships between money flow, staff size, and the number of enterprises managed by a corporation. Despite ignoring external shocks, our stability analysis reveals inherent instabilities in the system, highlighting significant risks for both venture success and staff employment. This model aims to support risk management by emphasizing the intrinsic sensitivity and potential instability in managing multiple enterprises. The methodology is based on the analysis of a system of differential equations, and the major contributions are a novel mathematical model and an explicit stability analysis with relevance to real-world situations.