Journal ArticleDOI
Collective Dynamics and Control of a 3-D Small-World Network with Time Delays
Xu Xu,Jiawei Luo,YuanTong Gu +2 more
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TLDR
In this paper, a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network is presented, where three control strategies, namely a position feedback control, a velocity feedback control and a hybrid control combined velocity with acceleration feedback, are introduced to stabilize this unstable system.Abstract:
The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems.read more
Citations
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Journal ArticleDOI
Dynamical model and control of a small-world network with memory
TL;DR: A dynamical model of influence volume of small-world-network with memory to investigate the effects of multiple delays on network dynamics shows delayed feedback control may find important applications in the management and dynamical control of complex networks.
Journal ArticleDOI
Stability, Instability and Bifurcation Modes of a Delayed Small World Network with Excitatory or Inhibitory Short-Cuts
TL;DR: The studies on the robustness stability show that the stability of this network is more robust to change of short-cut connections than the regular network, and the stability conditions from the proposed method are more conservational.
Journal ArticleDOI
Stability and instability of a neuron network with excitatory and inhibitory small-world connections
TL;DR: The proposed method can guarantee the stability of the system in most cases with random events, and is effective for cases where excitatory and inhibitory shortcuts exist simultaneously in the network.
Journal ArticleDOI
Insights into the inhibition and mechanism of compounds against LPS-induced PGE2 production: a pathway network-based approach and molecular dynamics simulations
Xinzhuang Zhang,Jiangyong Gu,Liang Cao,Yimin Ma,Su Zhenzhen,Fang Luo,Zhenzhong Wang,Na Li,Gu Yuan,Lirong Chen,Xiaojie Xu,Wei Xiao +11 more
TL;DR: A computational approach that integrates molecular docking and pathway network analysis (network efficiency and network flux) was developed to evaluate the efficacy of a compound against LPS-induced Prostaglandin E2(PGE2) production and has a good agreement with the experimental inhibitory potency.
Journal ArticleDOI
Dynamics and Control of a Delayed Oscillator Network by Pinning Strategy
TL;DR: This paper presents a detailed analysis on the dynamics and control of a delayed network by a pinning strategy and shows that the solutions of the original system can be obtained by the local dynamical behavior exhibiting in the transformed system.
References
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Journal ArticleDOI
Collective dynamics of small-world networks
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Journal ArticleDOI
Mean-field solution of the small-world network model.
TL;DR: A mean-field solution for the average path length and for the distribution of path lengths in the small-world network model is presented, which is exact in the limit of large system size and either a large or small number of shortcuts.
Book
Dynamics of Controlled Mechanical Systems with Delayed Feedback
H. Hu,Zaihua Wang +1 more
TL;DR: A model of delayed dynamic systems and the effects of a Short Time Delay on System Dynamics and Periodic Motions of Nonlinear Delay Systems are modeled.
Journal ArticleDOI
Delays, Connection Topology, and Synchronization of Coupled Chaotic Maps
TL;DR: It is shown that, similar to the undelayed case, the synchronization of the network depends on the connection topology, characterized by the spectrum of the graph Laplacian, which means that scale-free and random networks are capable of synchronizing despite the delayed flow of information.