A study on time-delay rumor propagation model with saturated control function

Abstract

Abstract In this paper, a time-delay rumor propagation model with a saturated control function is established. Regarding time delay as a bifurcation parameter, Hopf bifurcation is studied. By means of the normal form and the center manifold theorem, a formula is put forward to determine both Hopf bifurcation direction and bifurcating periodic solution stability, together with some numerical simulations to illustrate the relevant theoretical results. Simulation results indicate that an appropriate government control could make periodic oscillation behaviors of the system become steady so as to improve the balance of a social system.

Keywords

• rumor
• spread
• delay
• Hopf bifurcation