Bifurcation Analysis of an Advertising Diffusion Model

This research aims to investigate the impact of diffusion on the stability and bifurcation behavior of advertising diffusion systems. The study findings suggest that in the absence of diffusion, a higher proportion of crowd contact positively contributes to the stability of the system. Specifically, the study employs the interval partitioning method to discuss the k-mode Turing bifurcation and derives a more explicit Turing bifurcation line. Moreover, the study examines the k-mode Hopf bifurcation with the proportion of crowd contact acting as the bifurcation parameter. Furthermore, the weakly nonlinear analysis method is implemented to scrutinize the pattern formation in the Turing instability region. Finally, numerical simulation is utilized to validate the analytical findings obtained in this study.