A Dynamic Model of Talent Mobility in Higher Education with Time Delays and Multiplicative Noise: Stochastic Bifurcation and Stability Analysis

To investigate the underlying mechanisms of talent mobility in higher-education institutions influenced by factors such as the development environment, macroeconomic policies, and evaluation mechanisms, this paper proposes a nonlinear stochastic differential equation (SDE) dynamical model that incorporates time delays and multiplicative noise. We analyze the dynamic processes of talent mobility under varying conditions regarding the number of nodes, policy implementation cycles, and noise intensity. First, we employ central manifold theory and stochastic averaging methods to reduce the system to a one-dimensional averaged Ito^ equation. Subsequently, with τ as a parameter, we conduct an in-depth study of the system’s stochastic bifurcation behavior using the corresponding Fok–Planck–Kolmogorov equations. Finally, we validate the theoretical conclusions through numerical simulations. The results indicate that the number of nodes, policy delay, and noise intensity all have significant effects on system stability; an increasing delay induces random P-bifurcation in the system, and when N≤3 and N>3, the system exhibits distinctly different steady-state behaviors. We also found that excessively high noise intensity disrupts system stability, whereas moderate noise intensity has a positive effect on stability. This study not only provides theoretical insights into the dynamic evolution mechanisms of talent mobility in regional universities but also offers valuable guidance for universities in formulating talent recruitment and evaluation policies. The methodology employed in this study opens up a promising avenue for analyzing complex dynamic problems in the field of sociology.