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【期刊论文】Pinning a Complex Dynamical Network to Its Equilibrium
汪小帆, Xiang Li, Xiaofan Wang, Member, IEEE, and Guanrong Chen, Fellow
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: REGULAR PAPERS, VOL. 51, NO.10, OCTOBER 2004, 2074~2087,-0001,():
-1年11月30日
It is now known that the complexity of network topology has a great impact on the stabilization of complex dynamical networks. In this work, we study the control of random networks and scale-free networks. Conditions are investigated for globally or locally stabilizing such networks. Our strategy is to apply local feedback control to a small fraction of network nodes. We propose the concept of virtual control for microscopic dynamics throughout the process with different pinning schemes for both random networks and scale-free networks.We explain the main reason why significantly less local controllers are required by specifically pinning the most highly connected nodes in a scale-free network than those required by the randomly pinning scheme, and why there is no significant difference between specifically and randomly pinning schemes for controlling random dynamical networks. We also study the synchronization phenomenon of controlled dynamical networks in the stabilization process, both analytically and numerically.
Scale-free network,, random network,, virtual control,, stability,, synchronization.,
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【期刊论文】Anticontrol of chaos in continuous-time systems via time-delay feedback
汪小帆, Xiao Fan Wang, Guanrong Chen a, Xinghuo Yu,
Chaos, Vol. 10, No.4, 2000, 771~779,-0001,():
-1年11月30日
In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure.
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【期刊论文】Making a Continuous-Time Minimum-Phase System Chaotic by Using Time-Delay Feedback
汪小帆, Xiao Fan Wang, Guanrong Chen, and Kim. F Man
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 48, NO.5, MAY 2001, 641~645,-0001,():
-1年11月30日
A time-delay feedback control approach is developed for making a continuous-time minimum-phase system chaotic. The approach is based on the geometric control theory and a suitable approximate relationship between a time-delay differential equation and a discrete map. If the original system has an exponentially stable equilibrium point, then a simple time-delay output-feedback controller with arbitrarily small amplitude can drive the system chaotic. Two different types of simulation examples are included for demonstration.
Chaos,, minimum-phase,, time-delay.,
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56浏览
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【期刊论文】Generating Chaos in Chua's Circuit via Time-Delay Feedback
汪小帆, Xiao Fan Wang, Guo-Qun Zhong, Kit-Sang Tang, Kim F. Man, and Zhi-Feng Liu
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 48, NO.9, SEPTEMBER 2001, 1151~1156,-0001,():
-1年11月30日
A time-delay chaotification approach can be applied to the Chua's circuit by adding a small-amplitude time-delay feedback voltage to the circuit. The chaotic dynamics of this newly derived time-delay Chua's circuit is studied by theoretical analysis, verified by computer simulations as well as by circuit experiments.
Chaos,, stability,, time delay.,
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42浏览
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【期刊论文】Synchronization in Scale-Free Dynamical Networks: Robustness and Fragility
汪小帆, Xiao Fan Wang, Member, IEEE, and Guanrong Chen, Fellow
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 49, NO.1, JANUARY 2002, 54~62,-0001,():
-1年11月30日
Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions are in the power-law form. In this paper, we investigate the synchronization phenomenon in scale-free dynamical networks.We show that if the coupling strength of a scale-free dynamical network is greater than a positive threshold, then the network will synchronize no matter how large it is. We show that the synchronizability of a scale-free dynamical network is robust against random removal of nodes, but is fragile to specific removal of the most highly connected nodes.
Chaos,, graph,, network,, synchronization.,
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104浏览
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