ORIGINAL PAPERS

Bifurcation Analysis of an Advertising Diffusion Model

  • Yong Wang ,
  • Yao Wang ,
  • Liangping Qi
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  • Institute of Science and Technology, Tianjin University of Finance and Economics, Tianjin, 300222, China

Received date: 2023-08-10

  Revised date: 2023-11-01

  Accepted date: 2023-11-18

  Online published: 2024-03-01

Supported by

The authors would like to thank the editors and the anonymous reviewers for their valuable comments. This work is supported by the National Natural Science Foundation of China (Nos. 11701410 and 12001397) and the Natural Science Foundation of Tianjin City, China (No. 20JCQNJC00970).

Abstract

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.

Cite this article

Yong Wang , Yao Wang , Liangping Qi . Bifurcation Analysis of an Advertising Diffusion Model[J]. Communications on Applied Mathematics and Computation, 2025 , 7(4) : 1540 -1561 . DOI: 10.1007/s42967-023-00353-y

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