Extreme events on multiplex networks with asymmetric interlayer coupling

This study examines the transport dynamics and occurrence of extreme events within multiplex networks. We develop a multiplex network model characterized by asymmetric interlayer coupling, wherein the transition probabilities governing a walker’s movement between distinct layers are unequal. The corresponding master equation for the random walk process is formulated accordingly. Utilizing this framework, we derive a closed-form solution for the stationary node distribution under conditions of asymmetric interlayer coupling. Building upon this, we formulate analytical expressions for the probabilities of extreme events and the distribution of their magnitudes, employing the stationary distribution in conjunction with the binomial distribution. The concordance between analytical predictions and simulation outcomes reveals that the likelihood of extreme events escalates on layers exhibiting lower attractiveness, whereas it diminishes on layers with higher attractiveness. These results underscore the significant impact of asymmetric interlayer coupling on the distribution of extreme event risk across network layers. Furthermore, we introduce a control strategy specifically designed for multiplex networks with asymmetric interlayer coupling and assess its effectiveness using empirical data derived from real-world transportation systems. Collectively, these findings offer valuable insights for optimizing node capacity allocation and risk management in multilayer networks, thereby contributing to resilience-oriented design strategies aimed at enhancing the robustness of such systems against extreme events.