Journal
MATHEMATICS
Volume 10, Issue 19, Pages -Publisher
MDPI
DOI: 10.3390/math10193455
Keywords
rumor spreading model; delay; bifurcation; global stability; chaos
Categories
Funding
- National Science Foundation of China [71672154]
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By analyzing a delayed rumor-propagation model, this work investigates the existence and stability of the model's solutions and the rumor-endemic equilibrium. The study reveals that the delay can result in Hopf bifurcation and chaos.
In this work, we analyze a delayed rumor-propagation model. First, we analyze the existence and boundedness of the solution of the model. Then, we give the conditions for the existence of the rumor-endemic equilibrium. Regrading the delay as a bifurcating parameter, we explore the local asymptotic stability and Hopf bifurcation of the rumor-endemic equilibrium. By a Lyapunov functional technique, we examine the global asymptotically stability of the rumor-free and the rumor-endemic equilibria. We provide two control variables in the rumor-spreading model with time delay, and get the optimal solution via the optimal procedures. Finally, we present some numerical simulations to verify our theoretical predictions. They illustrate that the delay is a crucial issue for system, and it can lead to not just Hopf bifurcation but also chaos.
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