Stability and Hopf bifurcation analysis in DCTCP congestion control

Traditional loss-based transports cannot meet the strict requirements of low latency and high throughput in data center networks(DCNs).Thus data center transmission control protocol(DCTCP)is proposed to better manage the congestion control in DCNs.To provide insight into improving the stability of the DCN,this paper focuses on the Hopf bifurcation analysis of a fluid model of DCTCP,and investigates the stability of the network.The round-trip time(RTT),being an effective congestion signal,is selected as the bifurcation parameter.And the network turns unstable and generates periodic solutions when the parameter is larger than the given critical value,which is given by explicit algorithms.The analytical results reveal the existence of Hopf bifurcation.Numerical simulations are performed to make a comparative analysis between the fluid model and the simplified model of DCTCP.The influence of other parameters on the DCN stability is also discussed.

Selecting pinning nodes to control complex networked systems

One of the fundamental problems in pinning control of complex networks is selecting appropriate pinning nodes, such that the whole system is controlled. This is particularly useful for complex networks with huge numbers of nodes. Recent research has yielded several pinning node selection strategies, which may be efficient. However, selecting a set of pinning nodes and identifying the nodes that should be selected first remain challenging problems. In this paper, we present a network control strategy based on left Perron vector. For directed networks where nodes have the same in-and out-degrees, there has so far been no effective pinning node selection strategy, but our method can find suitable nodes. Likewise, our method also performs well for undirected networks where the nodes have the same degree. In addition, we can derive the minimum set of pinning nodes and the order in which they should be selected for given coupling strengths. Our proofs of these results depend on the properties of non-negative matrices and M-matrices. Several examples show that this strategy can effectively select appropriate pinning nodes, and that it can achieve better results for both directed and undirected networks.

Stability and bifurcation control of a neuron system under a novel fractional-order PD controller

In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative(PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally,numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.