Cascading crashes induced by the individual heterogeneity in complex networks

Abstract Deep understanding of the birth, growth and evolution of the real-life systems has been widely investigated, but the dynamics of system crashes are far beyond our knowledge. To this end, we propose a dynamical model to illustrate the collapsing behavior of complex networks, in which each node may leave the current networks since it has too few neighbors or has lost more than a specific proportion of its neighboring links. Different from previous works, the probability of being removed from the network for each node will be correlated with its original degree once the leaving conditions are satisfied, which includes the positive or negative correlation with the original degree, and totally independent probability deployment, and the individual heterogeneity has been integrated into these three probability setup schemes. Plenty of numerical simulations have indicated that the leaving probability setup scheme will greatly impact the system crashing behaviors under three different topologies including random, exponential and scale-free networks. In particular, the positively correlated scheme will substantially improve the survival of systems and further enhance the resilience of scale-free networks. To a great degree, the current results can help us to be further acquainted with the crashing dynamics and evolutionary properties of complex systems.

[1]  M. Benton,et al.  Rainforest collapse triggered Carboniferous tetrapod diversification in Euramerica , 2010 .

[2]  Zhen Wang,et al.  Heterogeneous Coupling between Interdependent Lattices Promotes the Cooperation in the Prisoner’s Dilemma Game , 2015, PloS one.

[3]  Jure Leskovec,et al.  Defining and evaluating network communities based on ground-truth , 2012, KDD 2012.

[4]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[5]  Hui-Jia Li,et al.  Social significance of community structure: Statistical view , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  H. Stanley,et al.  Breakdown of interdependent directed networks , 2016, Proceedings of the National Academy of Sciences.

[7]  Lev Muchnik,et al.  Identifying influential spreaders in complex networks , 2010, 1001.5285.

[8]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[9]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[10]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[11]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[12]  Aihua Li,et al.  Fast and Accurate Mining the Community Structure: Integrating Center Locating and Membership Optimization , 2016, IEEE Transactions on Knowledge and Data Engineering.

[13]  Shlomo Havlin,et al.  Origins of fractality in the growth of complex networks , 2005, cond-mat/0507216.

[14]  Jean-Philippe Bouchaud,et al.  Theory of collective opinion shifts: from smooth trends to abrupt swings , 2005, cond-mat/0504079.

[15]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[16]  Pavlin Mavrodiev,et al.  Social resilience in online communities: the autopsy of friendster , 2013, COSN '13.

[17]  Rogério de Souza Farias.  The cold war: a new history , 2006 .

[18]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[19]  B. Young,et al.  Response to Comment on "Status and Trends of Amphibian Declines and Extinctions Worldwide" , 2005, Science.

[20]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[21]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[22]  R. Pastor-Satorras,et al.  Generation of uncorrelated random scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[24]  Yi Yu,et al.  System crash as dynamics of complex networks , 2016, Proceedings of the National Academy of Sciences.

[25]  Yongtang Shi,et al.  On Wiener polarity index of bicyclic networks , 2016, Scientific Reports.

[26]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[27]  Dawei Zhao,et al.  Statistical physics of vaccination , 2016, ArXiv.

[28]  Zengqiang Chen,et al.  Risk Analysis and Enhancement of Cooperation Yielded by the Individual Reputation in the Spatial Public Goods Game , 2017, IEEE Systems Journal.

[29]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Hao Wang,et al.  Measuring robustness of community structure in complex networks , 2014, ArXiv.

[31]  Chao Li,et al.  Identification of influential spreaders based on classified neighbors in real-world complex networks , 2018, Appl. Math. Comput..

[32]  Matjaz Perc,et al.  Information cascades in complex networks , 2017, J. Complex Networks.

[33]  James P. Gleeson,et al.  Cascades on a class of clustered random networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[35]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[36]  Yongtang Shi,et al.  Note on two generalizations of the Randić index , 2015, Appl. Math. Comput..

[37]  Juan Wang,et al.  Inferring the reputation enhances the cooperation in the public goods game on interdependent lattices , 2017, Appl. Math. Comput..

[38]  C. Scott Findlay,et al.  Quantitative evidence for global amphibian population declines , 2000, Nature.

[39]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .