Dynamics of a delayed rumor spreading model with discontinuous threshold control

Chunru Li; Zujun Ma; Yuanyuan Wang

doi:10.1016/j.heliyon.2022.e11231

Dynamics of a delayed rumor spreading model with discontinuous threshold control

Heliyon. 2022 Oct 24;8(10):e11231. doi: 10.1016/j.heliyon.2022.e11231. eCollection 2022 Oct.

Authors

Chunru Li¹, Zujun Ma², Yuanyuan Wang¹

Affiliations

¹ Business School, Changshu Institute of Technology, Changshu, 215500, China.
² School of Economics and Management, Southwest Jiaotong University, Chengdu, 610031, China.

Abstract

In this paper, we studied a delayed rumor spreading model with discontinuous threshold control. First, we studied the existence of equilibria of the subsystem. Regarding the delay as bifurcating parameter, the local asymptotic stability and Hopf bifurcation of the positive equilibrium are discussed by analyzing the corresponding characteristic equations of linearized systems. Then, we studied the existence of the sliding mode and analyzed the existence of the tangent equilibria, boundary equilibria, regular equilibria, and the stability of the pseudo-equilibrium. Finally, we provide some numerical simulations to verify the theoretical results.

Keywords: Delay; Discontinuous control; Hopf bifurcation; Rumor spreading.