Individuals' Different Behaviors Induce Rich And Colorful Overall Behaviors On Complex Networks

In recent years, the newborn of complex networks and the dynamics of complex networks have been paid more and more attentions by researchers. It is because that many complex systems in real world can be described in forms of complex networks. Typical examples include social networks among population, airport networks, World Wide Web, Internet, power grids networks, collaboration networks, metabolic networks and genetic regulatory networks and so on. Therefore, the study on the statistical characteristics of complex networks and their dynamic behaviors become a research hotspot in the science of complexity.In this thesis, the effects of individuals'different behaviors on the overall behaviors on complex networks are studied, including the spread of epidemic on complex networks and evolutionary game on complex networks, respectively. Concretely, it includes several aspects as follows:Firstly, the effects of individual behaviors and the structures of networks on the dynamics of epidemic and the control effects under voluntary vaccination mechanism are investigated.1, the influence of the voluntary vaccination mechanism on different topologies of networks is studied. Under voluntary vaccination mechanism, each individual knows that the risk of being infected is proportional to its degree, so the nodes with large degrees (hub nodes) are more willing to take vaccination. Thus, in such case, the control effects on scale-free network are better than on the random network.2, two different risk assessment systems are established by the technique of dynamic programming, and then study the impacts of the two different systems on the individual behaviors, consequently, on the dynamics of epidemic. One is that each individual estimates the risk of infection in a uniform way, that is, irrelevant to the degrees of nodes. Another is that the risk of being infected for each individual is related to the degree of itself. By investigating the two different estimation systems, we find that the two different estimation systems can yield distinct effects on the dynamics of epidemic and control efforts.Secondly, the co-evolution of the spread of epidemic and the contact network is studied. Facing the outbreaks of infectious diseases, people often reduce the outside activities to avoid the risk of being infected. However, once the prevalence of disease is minimal, people will recover their norm life. So we assume that individuals adjust their contact patterns according to the perceived risk from disease. Some links are cut if the risks of infection are high, whereas, some original broken links will be recover again. Meanwhile the effects of the lag of information of disease for individuals on the dynamics of epidemic are also considered. We find that, under certain conditions, both structure of network and the transmission of epidemic can pass from steady state to periodic oscillation via Hopf bifurcation. Thirdly, the effects of the memory-based learning capability on the coverage of vaccination and on the final epidemic size are considered. By investigations, we find that individual's memory-based learning capability is a double-edged sword for society. If the cost of vaccination is low, the larger of the learning capabilities of individuals, the higher coverage of vaccination and then lower coverage of diseases. Yet, if the cost of vaccination is high, the zeal of vaccination is hindered for stronger learning capability, so the outbreaks of diseases.Fourthly, we assume that susceptible individuals can switch their states between the unprotected state ( S_u) and the protected state ( S_p) relying on their perceived risk of diseases. The transition probability from S_uto S_pincreases with the number of infections they acquired. On the contrary, the transition probability from S_pto S_pdecreases with the number of infections they acquired. Meanwhile, we assume that the acquired information by individuals has a certain time lag. By Monte Carlo method and Markov chain method, we find that the time-delayed information of diseases can induce the periodic outbreaks of infectious diseases.Fifthly, how the aspiration of individuals affects the frequency of cooperation on evolutionary games is studied.1, for prisoner's dilemma game, individuals learning motivation are defined relying on their aspiration payoffs. The higher the aspiration payoffs and the higher learning motivation of individuals, otherwise opposite situation occurs. We find that moderate aspiration can induce the highest level of cooperation, yet too large or too small aspiration is not favorable to cooperation. Also the impact of noise on the frequency of cooperation is studied and find that there exits the stochastic resonance phenomenon.2, some large corporations often extend their business to different regions to pursue their maximal profit. However, once the profit gained from one region is undesirable, they will withdraw the investment partially or entirely, and then transfer to other regions. Inspired by such interesting phenomena, we consider a co-evoluation model in spatial public goods game where the probability of reconnection depends on the aspiration payoffs of individuals. Namely, the reconnection probability is proportional to the aspiration payoffs of individuals. We find that the highest frequency of cooperation can emerge when the aspiration payoff is proper given. At the same time, by investigating the degree of networks, we find the network is a heterogeneous network, so the optimal phenomenon can be well explained.