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.