Interplay Between Spreading Dynamics And Biased Walk In Multilayer Networks

Spreading processes commonly exist in our real world.Among them,the spreading of infectious diseases and rumors has caused serious impact on human health and social security.If we understand the spreading mechanism,it will provide a strong theoretical basis for the prevention and control of the spreading processes.Therefore,it is of great significance to study the spreading mechanism of these spreading processes.In order to describe the contact relationship of communication in detail,some scholars have introduced the single-layer network to study the spreading process.However,due to the complexity of the real world,the single-layer network can not be well used to describe the complex systems,so scholars have introduced the multi-layer network.This thesis focuses on the spreading process based on multi-layer networks.In the main study of this thesis,we propose a spreading model in mul-tilayer networks and study the nature of nonequilibrium phase transition in the model.The model integrates the susceptible-infected-susceptible(or susceptible-infected-recovered)spreading dynamics with a biased diffusion process among different layers.A parameter ? is introduced to control the bias of the dif-fusion process,such that each individual prefers to move to one layer with more infected(or recovered)neighbors for larger values of a.Using stochastic simulations and mean-field theory,we show t.hat the type of phase transition from a disease-free phase to an endemic phase(EP)depends on the value of?.When a is small enough,the system undergoes a usual continuous phase transition as an effective spreading rate? increases,as in single-layer networks.Interestingly,when ? exceeds a critical value the system shows either a hybrid two-step phase transition or a one-step discontinuous phase transition as? in-creases.The former contains a continuous transition between the disease-free phase and a low-prevalence EP,and a discontinuous transition between the low-prevalence EP and a high-prevalence EP.For the latter,only a discontinu-ous transition occurs from the disease-free phase directly to the high-prevalence EP.Moreover,we show that the discontinuous transition is always accompanied by a spontaneous symmetry breaking in occupation probabilities of individuals in each layer.