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- Title
Stability and Hopf Bifurcation Analyses of a Delayed Rumor Spreading Model and Its Discontinuous Control.
- Authors
Zhu, Honglan; Zhang, Xuebing; Wang, Ling
- Abstract
In this paper, a delayed rumor propagation model with a discontinuous control mechanism is investigated. First, we investigate the model's existence and boundedness. Then, conditions for the existence of the rumor-endemic equilibrium are derived utilizing differential inclusions. We examine the local asymptotic stability and Hopf bifurcation of the rumor-endemic equilibrium when the discontinuous control function is differential at the rumor-endemic equilibrium, considering the delay as the bifurcating parameter. When the discontinuous control function is not differential at the rumor-endemic equilibrium, we investigate the global asymptotically stable rumor-free and rumor-endemic equilibria using the Lyapunov functional technique. We conclude by providing two examples to validate our theoretical predictions. It is demonstrated that delay is a critical system parameter that can result in both Hopf bifurcation and chaos.
- Subjects
BIFURCATION diagrams; HOPF bifurcations; RUMOR; DIFFERENTIAL inclusions; DISCONTINUOUS functions
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2022, Vol 32, Issue 16, p1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S021812742250242X