复杂网络上个体的不同行为导致多样的整体行为
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摘要
对近年兴起的复杂网络及其上动力学行为的研究受到越来越多的关注,这是由于真实世界中的很多复杂系统都可以抽象为相互作用的个体组成的网络。例如:人与人之间的社会关系网、航空网、万维网、Internet网、电力网、科学家合作网、新陈代谢网、基因调控网等等。因此,对复杂网络的统计特征以及其上的动力学行为的研究成为复杂性科学中的一个研究热点。
本论文主要研究复杂网络上各种个体行为对网络整体动力学行为的影响,包括网络上的传染病动力学和演化博弈动力学。具体包括以下几个方面:
一、研究自愿接种机制下个体行为和网络结构对传播过程以及预防控制效果的影响。
1,研究自愿接种机制在不同网络上产生的不同效果。由于在自愿接种机制下每个个体能认识到自己被感染的风险正比与自身的度,所以度大的节点更愿意采取接种。因此自愿接种机制在无标度网络上的效果比在随机网络上的效果好。
2,利用动态规划方法建立两种不同的风险评价体系,然后研究这两种评价体系对个体行为产生的影响,进而对动力学特征的影响。一种评价体系是统一评价体系——所有个体认为被感染的风险是一样的,即与节点度无关,另外一种风险评价体系是偏爱性评价体系——个体认为被感染的风险正比与自身的节点度。通过研究发现两种风险评价体系会对传播动力学产生本质的差别。
二、研究复杂网络上的传播动力学和网络的共同演化。当疾病爆发的时候人们会减少和外面的接触,一旦疾病的风险减低时他们又会恢复原来的生活方式。因此我们假设网络中个体根据对疾病风险的了解程度决定是断边还是恢复一部分原来被断的边。同时研究了时间滞后性对传播行为的影响。通过研究发现网络结构和疾病的动力学过程在一定条件下会通过霍夫分岔从稳定状态转化到周期演化。
三、研究具有记忆能力的模仿机制对整体的接种范围和传播范围的影响。通过研究发现个体具有记忆能力的模仿机制对社会是一把双刃剑。当接种代价比较小的时候,记忆能力越强,接种范围越广,因而感染比例越少。反之,当接种代价比较大的时候,记忆能力越强反而会降低接种的积极性,从而不能有效的抑制疾病传播。
四、假设易感染者根据他们了解到的疾病信息可以在两种不同状态-----无保护态( S_u)和保护态( S_p)之间相互转化。从S_u到S_p的转移概率随着感染人数的增加而增加,反之,从S_p到S_u的转移概率随着感染人数的增加而减小。同时,我们假设个体对疾病风险信息的了解具有一定的时间滞后性。通过Monte Carlo方法和Markov chain方法研究发现,基于滞后信息的状态转化会导致传染病的周期爆发。
五、个体的期望收益对演化博弈中合作行为的影响。
1,对于囚徒困境博弈,定义网络中个体的学习意愿与自身对收益的期望值有关,期望收益越高则学习意愿越高,反之则越小。通过研究发现适当的期望值可以促进最优的合作频率。同时研究了噪音对合作频率的影响,发现随机共振现象。
2,考虑到很多大型公司往往在不同的地区都有他们的业务。如果在某个地区的业务不能达到他们预期的期望值,这些公司很有可能取消在这个地区的业务而转投到其他的地区。受此启发,我们假定空间公共物品博弈上断边重连的概率依赖于个体的期望收益,当期望收益比较低的时候,断边概率很小,反之断边重连概率大。研究发现适当的期望收益可以促进最优的合作频率。同时通过研究网络的度分布,我们发现适当的期望对应的网络是一个异质性的网络,因此可以很好的解释出现最优合作频率的原因。
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.
本论文主要研究复杂网络上各种个体行为对网络整体动力学行为的影响,包括网络上的传染病动力学和演化博弈动力学。具体包括以下几个方面:
一、研究自愿接种机制下个体行为和网络结构对传播过程以及预防控制效果的影响。
1,研究自愿接种机制在不同网络上产生的不同效果。由于在自愿接种机制下每个个体能认识到自己被感染的风险正比与自身的度,所以度大的节点更愿意采取接种。因此自愿接种机制在无标度网络上的效果比在随机网络上的效果好。
2,利用动态规划方法建立两种不同的风险评价体系,然后研究这两种评价体系对个体行为产生的影响,进而对动力学特征的影响。一种评价体系是统一评价体系——所有个体认为被感染的风险是一样的,即与节点度无关,另外一种风险评价体系是偏爱性评价体系——个体认为被感染的风险正比与自身的节点度。通过研究发现两种风险评价体系会对传播动力学产生本质的差别。
二、研究复杂网络上的传播动力学和网络的共同演化。当疾病爆发的时候人们会减少和外面的接触,一旦疾病的风险减低时他们又会恢复原来的生活方式。因此我们假设网络中个体根据对疾病风险的了解程度决定是断边还是恢复一部分原来被断的边。同时研究了时间滞后性对传播行为的影响。通过研究发现网络结构和疾病的动力学过程在一定条件下会通过霍夫分岔从稳定状态转化到周期演化。
三、研究具有记忆能力的模仿机制对整体的接种范围和传播范围的影响。通过研究发现个体具有记忆能力的模仿机制对社会是一把双刃剑。当接种代价比较小的时候,记忆能力越强,接种范围越广,因而感染比例越少。反之,当接种代价比较大的时候,记忆能力越强反而会降低接种的积极性,从而不能有效的抑制疾病传播。
四、假设易感染者根据他们了解到的疾病信息可以在两种不同状态-----无保护态( S_u)和保护态( S_p)之间相互转化。从S_u到S_p的转移概率随着感染人数的增加而增加,反之,从S_p到S_u的转移概率随着感染人数的增加而减小。同时,我们假设个体对疾病风险信息的了解具有一定的时间滞后性。通过Monte Carlo方法和Markov chain方法研究发现,基于滞后信息的状态转化会导致传染病的周期爆发。
五、个体的期望收益对演化博弈中合作行为的影响。
1,对于囚徒困境博弈,定义网络中个体的学习意愿与自身对收益的期望值有关,期望收益越高则学习意愿越高,反之则越小。通过研究发现适当的期望值可以促进最优的合作频率。同时研究了噪音对合作频率的影响,发现随机共振现象。
2,考虑到很多大型公司往往在不同的地区都有他们的业务。如果在某个地区的业务不能达到他们预期的期望值,这些公司很有可能取消在这个地区的业务而转投到其他的地区。受此启发,我们假定空间公共物品博弈上断边重连的概率依赖于个体的期望收益,当期望收益比较低的时候,断边概率很小,反之断边重连概率大。研究发现适当的期望收益可以促进最优的合作频率。同时通过研究网络的度分布,我们发现适当的期望对应的网络是一个异质性的网络,因此可以很好的解释出现最优合作频率的原因。
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.
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