Dynamics of the congestion control model in underwater wireless sensor networks with time delay. (English) Zbl 1372.90021
Summary: In this paper, a congestion control model in underwater wireless sensor network with time delay is considered. First, the boundedness of the positive equilibrium, where the samples density is positive for each node and the different event flows coexist, is investigated, which implies that the samples density of sensor node cannot exceed the Environmental carrying capacity. Then, by considering the time delay can be regarded as a bifurcating parameter, the dynamical behaviors, which include local stability and Hopf bifurcation, are investigated. It is found that when the communication time delay passes a critical value, the system loses its stability and a Hopf bifurcation occurs, which means the underwater wireless sensor network will be congested, even collapsed. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some numerical examples are finally performed to verify the theoretical results.
MSC:
| 90B10 | Deterministic network models in operations research |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 37M05 | Simulation of dynamical systems |
Keywords:
underwater wireless sensor networks; time delay; stability; bifurcation; congestion controlReferences:
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