首页|Spontaneous Recovery in Directed Dynamical Networks
Spontaneous Recovery in Directed Dynamical Networks
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Complex networked systems,which range from biological systems in the natural world to infrastructure systems in the human-made world,can exhibit spontaneous recovery after a failure;for example,a brain may spontaneously return to normal after a seizure,and traffic flow can become smooth again after a jam.Previous studies on the spontaneous recovery of dynamical networks have been limited to undi-rected networks.However,most real-world networks are directed.To fill this gap,we build a model in which nodes may alternately fail and recover,and we develop a theoretical tool to analyze the recovery properties of directed dynamical networks.We find that the tool can accurately predict the final fraction of active nodes,and the prediction accuracy decreases as the fraction of bidirectional links in the network increases,which emphasizes the importance of directionality in network dynamics.Due to different ini-tial states,directed dynamical networks may show alternative stable states under the same control parameter,exhibiting hysteresis behavior.In addition,for networks with finite sizes,the fraction of active nodes may jump back and forth between high and low states,mimicking repetitive failure-recovery pro-cesses.These findings could help clarify the system recovery mechanism and enable better design of net-worked systems with high resilience.
School of Artificial Intelligence and Automation & The MOE Engineering Research Center of Autonomous Intelligent Unmanned Systems & the Key Laboratory of Image Processing,Huazhong University of Science and Technology,Wuhan 430074,China
Center for Polymer Studies,Department of Physics,Boston University,Boston,MA 02215,USA
National Natural Science Foundation of ChinaScience and Technology Project of the State Grid Corporation of China
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