Advances in Complex Systems

This paper studies the bounded confidence model on growing fully-mixed populations. In this model, in addition to the usual opinion clusters, significant secondary clusters of smaller size appear systematically, while those secondary clusters appear erratically and include much fewer agents when the population is fixed. Through simulations, we derive the bifurcation diagram of the growing population model and compare it to the diagram obtained with an evolving probability density instead of agents, and with their equivalent having a fixed population. Our tests, when changing the usual bounded confidence function into a smooth bounded confidence function, suggest that these secondary clusters are mainly generated by a different mechanism when the population is growing than when it is fixed.

The research on efficient routing strategies holds paramount importance in mitigating network congestion and enhancing the transmission capacity of complex networks. A Hierarchical Routing Optimization (HRO) strategy is proposed for dual-layer networks featuring both logical and physical layer structures. This strategy employs distinct methods for packet transmission at the logical and physical layers to optimize the utilization of network resources. Comparison with the improved static-weighted routing strategy (ISWR) and the improved effective routing strategy (IER) involves analyzing the relationship between the transmission capacity of the dual-layer network and the coupling method under these three routing strategies. This analysis aims to determine the optimal coupling method for the routing strategy, thereby enhancing overall network capacity. The simulation results reveal that the random coupling method proves most effective when employing the ISWR strategy, the assortative coupling method excels with the IER strategy, and the dissortative coupling method stands out when implementing the HRO strategy. In evaluating the ISWR strategy, IER strategy, and HRO strategy, it becomes evident that the HRO strategy substantially amplifies the transmission capacity of the dual-layer network. Furthermore, the HRO strategy exhibits heightened robustness against both random and deliberate attacks compared to the IER strategy.

In the spatial public goods game (SPGG), punishment effectively promotes cooperation but often reduces the collective benefits of cooperators and punishers. In order to increase revenue, we propose a probabilistic interaction domain model considering both strategy type and payoff level. In this model, players are divided into two types, successful players with payoffs higher than the payoff threshold and failed players with payoffs lower than the payoff threshold. A successful player is less likely to change the interaction range than a failed player. Through extensive simulations, it is shown to verify that a higher payoff threshold leads to a more pronounced promotion effect on cooperation and corresponds to a higher cooperation return. Moreover, introducing dynamic interaction domain can rapidly remove defectors from the vicinity of cooperative players on regular lattices. Reducing the payoff gap between punishers and cooperators helps mitigate the system’s second-order free-riding problem. Additionally, through analysis of the critical parameters, it is revised that incorporating diversity in interaction structures substantively enhances cooperation level.

Network robustness, which includes controllability robustness and connectivity robustness, reflects the ability of a network system to withstand attacks. In this paper, a Graph Convolutional Network (GCN) approach is proposed for predicting network robustness. In contrast to the existing Convolutional Neural Network (CNN) approach, the network topology and the node characteristics are directly used as GCN input without being converted into a grayscale image. Due to the reduction in the number of feature maps, the model size of a GCN is greatly reduced to only 1% of a CNN. Extensive experimental studies on four representative networks and six real networks have proven that the proposed approach can achieve better predictive performance with less training and running time.