Abstract
Hopf bifurcation for an SEIRS-V model with delays on the transmission of worms in a wireless sensor network is investigated. We focus on existence of the Hopf bifurcation by regarding the diverse delay as a bifurcation parameter. The results show that propagation of worms in the wireless sensor network can be controlled when the delay is suitably small under some certain conditions. Then, we study properties of the Hopf bifurcation by using the normal form theory and center manifold theorem. Finally, we give a numerical example to support the theoretical results.
Highlights
In recent years, wireless sensor networks have received extensive attention due to their vast potential in many application environments
The generalization of the delayed SEIRSV model describing worms spreading in a wireless sensor network investigated in [11] by inserting the latent period delay in the exposed sensor nodes has been considered
We find that τ1 and τ2 can influence stability of system (4) and make system (4) undergo a Hopf bifurcation under some certain conditions
Summary
Wireless sensor networks have received extensive attention due to their vast potential in many application environments. In [10], Mishra and Keshri proposed the following SEIRS-V model to describe the propagation of worms in a wireless sensor network: dS (t) dt. Considering that there is a latent period of worms in the exposed nodes in system (3), we study the following system with delays:. − ηV (t − τ2) , where τ1 is the time delay due to the latent period of worms in the exposed nodes and τ2 is the time delay due to the period that the antivirus software uses to clean worms in the infected nodes and that due to the temporary immunity period of the recovered and the vaccinated nodes.
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