A Dynamical System Approach to Language Bias Evolution on Complex Networks

We propose a dynamical systems model to study language competition and bias evolution in structured agent populations. Each agent is characterized by a continuous bias variable representing their linguistic preference, evolving under the combined influence of peer interactions, native language retention, and external prestige forces. The model incorporates a nonlinear damping mechanism that confines the agent's bias within a fixed range between negative one and one, and allows for heterogeneous susceptibility and retention parameters. We analyze the model in its linear regime and perform a stability analysis of the fixed points under both symmetric and asymmetric network topologies. Simulations on fully connected and small-world networks reveal diverse dynamical scenarios, including language death, bilingual persistence, and spontaneous population bifurcation into opposing linguistic groups. The results provide insight into the interplay of social structure, identity, and external influence in shaping language dynamics.