Cascade Collapse Dynamics On Two-Layer Correlation Network

Most of the networks in real life are coupled together.Since the network system is open,there are both information exchange between nodes in the system and energy exchange with the external environment.Sometimes the damage caused by some sudden small disturbances is huge.Once a large-scale cascading failure occurs,the consequences are unimaginable,especially the losses caused to interconnected networks.With the help of network science,modeling the cascade dynamic behavior on complex networks has become an important research topic.For this reason,this paper proposes a new dynamic model to further explore the dynamic behavior of the cascade collapse of the two-layer correlation network.The main innovative work is divided into the following two parts:(1)A new decision logic-"XOR" logic is proposed for interconnected networks.This logic is used to link the cascading processes of interconnected networks,and at the same time two new node leaving rules are proposed: overall rules and independent rules.The experimental results show that under the "XOR" judgment condition,the two leaving rules will cause the system to appear pseudo-steady state and sudden collapse.At the same time,the results show that under the overall leaving rule,the system will have two critical thresholds,that is,there is a critical threshold.qth1 makes the system change from a non-crash state to a crash state;there is also a critical threshold qth2,which makes the system change from a crash state to a non-crash state.At the same time,it is found that positive correlation mapping can improve system stability more than random mapping and negative correlation mapping.The simulation results also show that the combination of individuals with similar comprehensive ability or homogeneity(similar to positive correlation mapping)is more conducive to the stability of the network(similar to the marriage relationship network).(2)The compensation mechanism is introduced into the cascade dynamics of the two-layer correlation network,and two compensation mechanisms are considered:one-way compensation and two-way compensation.Through a large number of numerical simulations,the effects of network settings,mapping relationships,compensation ratios,and departure probability on the experimental results are studied.The research results show that in one-way compensation,the introduction of compensation mechanisms in the same configuration of the upper and lower layers of the network can significantly improve the performance of the compensated network.In the different configurations of the upper and lower layers of the network,the heterogeneity of the network makes the compensation effect insignificant,and the mapping relationship has little effect on the result.In the two-way compensation mechanism,the experimental results show that the positive correlation mapping can make the system more stable than the negative correlation mapping and random mapping,and the ER-ER network configuration is more competitive when the average connection density is given.The leaving probability will affect the performance of the network.The higher the node leaving probability,the lower the system performance.In summary,the dynamic laws and characteristics in the collapse of the network cascade revealed in this article will help people further understand the dynamics of interconnected networks.