Network switching can improve system order

Building upon the theoretical framework of Parrondo's games, this study explores the impact of network dynamic switching, particularly in multilayer networks, on system order. Two 9-node multilayer network systems were constructed, accompanied by the design of an update rule for individual states. System entropy was used as an evaluation index for system order, and a theoretical analysis of system entropy was conducted using the discrete Markov chain method. The findings indicate that switching between multilayer networks effectively enhances system order. Furthermore, simulation results show that in multilayer BA scale-free network systems, network switching further contributes to the enhancement of system order. The coupling and network switching of multilayer networks may complement each other in enhancing the internal order of the system. Coupling enhances the synergy between different network layers, while network switching increases entanglement and mutual information between individuals and their small habitats. This dual mechanism reduces the diversity of system states and promotes greater internal order.