Complex Dynamical Analysis of Two Factors of Fractional-Order Conflict Model With Time Delay and Feedback Control Strategy: With Focus on China’s Internet Conflicts

This paper will go beyond the traditional case study method used by most of the existing literature on Chinese internet conflict: instead, a mathematical model will be developed to explore the dynamics of the conflict, establishing a new delayed two-factor fractional-order model with feedback controls. Two important dynamical properties of this model, its stability and its oscillations, are investigated. Finally, during numerical simulations, the critical values of bifurcation are accurately calculated, and both the numerical simulation and theoretical analysis are then applied to the Chinese internet conflict to illustrate the applicability of the findings. The effects of time delays are elucidated. The model is applied to a real-world problem, demonstrating the practical relevance of the findings: a Sina Weibo case of a gender-related controversy, linking model states to observed burst-decay posting patterns. Under benchmark parameters, increasing the delay induces a Hopf bifurcation; in the empirical case study, the estimated critical delay is about 0.5390 h, and feedback controls attenuate oscillations.