Opinion dynamics with highly oscillating opinions

Opinion Dynamics (OD) models are a class of agent-based models that describe how opinions evolve within a population. In these models, individual opinions change through interactions governed by an opinion fusion rule that specifies how updates occur. Despite their simplicity, OD models offer interpretable mechanisms for understanding the collective dynamics of opinion formation. However, most existing approaches focus on the emergence of consensus, fragmentation, or polarization, while overlooking real-world scenarios characterized by highly oscillatory trends. This study addresses this limitation by evaluating the ability of several OD models extended with dynamic parameters to reproduce oscillatory dynamics. To this end, we formulate an optimization problem solved via evolutionary algorithms. The methodology is first validated on synthetic target series to assess the intrinsic oscillatory capabilities of the models, and subsequently applied to a real-world dataset of public opinion about immigration, drawn from the monthly barometer of the Spanish Sociological Research Center. Results show that the Agent-independent Time-based Bounded Confidence and Repulsion (ATBCR) model, which combines confidence-based and polarization-based update mechanisms, achieves the best performance. The optimized model closely reproduces historical opinion fluctuations while exhibiting interpretable, human-like patterns of collective evolution.