Critical transitions in heterogeneous networks: Loss of low-degree nodes as an early warning signal.

A large number of real networks show abrupt phase transition phenomena in response to environmental changes. In this case, cascading phenomena can induce drastic and discontinuous changes in the system state and lead to collapse. Although complex network theory has been used to investigate these drastic events, we are still unable to predict them effectively. We here analyze collapse phenomena by proposing a minimal two-state dynamic on a complex network and introducing the effect of local connectivities on the evolution of network nodes. We find that a heterogeneous system of interconnected components presents a mixed response to stress and can serve as a control indicator. In particular, before the critical transition point is reached a severe loss of low-degree nodes is observed, masked by the minimal failure of higher-degree nodes. Accordingly, we suggest that a significant reduction in less connected nodes can indicate impending global failure.

[1]  Wei Wang,et al.  Unification of theoretical approaches for epidemic spreading on complex networks , 2016, Reports on progress in physics. Physical Society.

[2]  Alessandro Vespignani,et al.  Reaction–diffusion processes and metapopulation models in heterogeneous networks , 2007, cond-mat/0703129.

[3]  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.

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

[5]  D C Spray,et al.  Biophysical properties of gap junctions between freshly dispersed pairs of mouse pancreatic beta cells. , 1991, Biophysical journal.

[6]  Front , 2020, 2020 Fourth World Conference on Smart Trends in Systems, Security and Sustainability (WorldS4).

[7]  Alessandro Giuliani,et al.  Why network approach can promote a new way of thinking in biology , 2014, Front. Genet..

[8]  J. Trosko,et al.  The gap junction as a “Biological Rosetta Stone”: implications of evolution, stem cells to homeostatic regulation of health and disease in the Barker hypothesis , 2011, Journal of Cell Communication and Signaling.

[9]  Alessio Gizzi,et al.  Role of topology in complex functional networks of beta cells. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Kristina Lerman,et al.  Degree Correlations Amplify the Growth of Cascades in Networks , 2018, Physical review. E.

[11]  S. Carpenter,et al.  Anticipating Critical Transitions , 2012, Science.

[12]  Alessio Gizzi,et al.  On the coherent behavior of pancreatic beta cell clusters , 2014, 1407.7741.

[13]  Wei Wang,et al.  Emergence of hysteresis loop in social contagions on complex networks , 2017, Scientific Reports.

[14]  Peter Sheridan Dodds,et al.  Information cascades on degree-correlated random networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  S. Carpenter,et al.  Early-warning signals for critical transitions , 2009, Nature.

[16]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Tao Zhou,et al.  Interactive social contagions and co-infections on complex networks. , 2018, Chaos.

[18]  Yunpeng Wang,et al.  Percolation transition in dynamical traffic network with evolving critical bottlenecks , 2014, Proceedings of the National Academy of Sciences.

[19]  Frank Schweitzer,et al.  How damage diversification can reduce systemic risk. , 2015, Physical review. E.

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

[21]  J. Bascompte,et al.  Critical slowing down as early warning for the onset of collapse in mutualistic communities , 2014, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Sergey N. Dorogovtsev,et al.  Critical phenomena in complex networks , 2007, ArXiv.

[23]  A. Charollais,et al.  Connexins protect mouse pancreatic β cells against apoptosis. , 2011, The Journal of clinical investigation.

[24]  Zbigniew R Struzik,et al.  Phase transition in a healthy human heart rate. , 2005, Physical review letters.

[25]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[26]  M. G. Pedersen,et al.  Gap-junction coupling and ATP-sensitive potassium channels in human β-cell clusters: Effects on emergent dynamics. , 2017, Physical review. E.

[27]  D. Borsboom,et al.  Critical slowing down as early warning for the onset and termination of depression , 2013, Proceedings of the National Academy of Sciences.

[28]  S. Filippi,et al.  Mathematical modeling of gap junction coupling and electrical activity in human β-cells , 2015, Physical biology.

[29]  T. Nagatani.  The physics of traffic jams , 2002 .

[30]  J. Gleeson,et al.  Seed size strongly affects cascades on random networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  M. Scheffer,et al.  Slowing down as an early warning signal for abrupt climate change , 2008, Proceedings of the National Academy of Sciences.

[32]  H. Stanley,et al.  Spontaneous recovery in dynamical networks , 2013, Nature Physics.

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

[34]  S V Buldyrev,et al.  Self-organized complexity in economics and finance , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Zbigniew R Struzik,et al.  Criticality and phase transition in stock-price fluctuations. , 2006, Physical review letters.

[36]  Flaviano Morone,et al.  Model of brain activation predicts the neural collective influence map of the brain , 2017, Proceedings of the National Academy of Sciences.

[37]  Paolo Meda,et al.  Loss of connexin36 channels alters beta-cell coupling, islet synchronization of glucose-induced Ca2+ and insulin oscillations, and basal insulin release. , 2005, Diabetes.

[38]  P. Meda.  The In Vivo β-to-β-Cell Chat Room: Connexin Connections Matter , 2012, Diabetes.