We focus on the effects of individuals＇ degrees on spontaneous cooperation. By investigating evolutionary PDGs on random networks with two distinct degrees, we find some resonance-type behaviors of the cooperator fre...We focus on the effects of individuals＇ degrees on spontaneous cooperation. By investigating evolutionary PDGs on random networks with two distinct degrees, we find some resonance-type behaviors of the cooperator frequency with the variation of degree. We also find that increasing hums degree actually disfavors the cooperation though the heterogeneity in degree can enhance cooperation in the population.展开更多
The Ott-Antonsen ansatz provides a powerful tool in investigating synchronization among coupled phase oscil- lators. However, previous works using the ansatz only focused on the evolution of the order parameter and th...The Ott-Antonsen ansatz provides a powerful tool in investigating synchronization among coupled phase oscil- lators. However, previous works using the ansatz only focused on the evolution of the order parameter and the information on desynchronized oscillators is less discussed. In this work, we show that the Ott-Antonsen ansatz can also be applied to investigate the desynchronous dynamics in coupled phase oscillators. Studying the original Kuramoto model and two of its variants, we find that the dynamics of α（ω）, the coefficient in the Fourier series of the probability density, can give most of the information on the synchronization, for example, the threshold of natural frequency delimiting the oscillators synchronized and desychronized by the mean field, the formulation of the effective frequency ωe （ω） of desynchronous oscillators, and the structure of the graph ωe （ω）.展开更多
We investigate the evolutionary prisoner’s dilemma game in structured populations by introducing dimers,which are defined as that two players in each dimer always hold a same strategy.We find that influences of dimer...We investigate the evolutionary prisoner’s dilemma game in structured populations by introducing dimers,which are defined as that two players in each dimer always hold a same strategy.We find that influences of dimerson cooperation depend on the type of dimers and the population structure.For those dimers in which players interactwith each other,the cooperation level increases with the number of dimers though the cooperation improvement leveldepends on the type of network structures.On the other hand,the dimers,in which there are not mutual interactions,will not do any good to the cooperation level in a single community,but interestingly,will improve the cooperationlevel in a population with two communities.We explore the relationship between dimers and self-interactions and findthat the effects of dimers are similar to that of self-interactions.Also,we find that the dimers,which are establishedover two communities in a multi-community network,act as one type of interaction through which information betweencommunities is communicated by the requirement that two players in a dimer hold a same strategy.展开更多
We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner＇s dilemma game （PDG） in one l...We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner＇s dilemma game （PDG） in one layer and snowdrift game （SDG） in the other. We explore the dependences of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer. Moreover, in contrast to the result for PDG in single-layer square lattices, the parameter regime where cooperation could be maintained expands significantly in the PDG layer. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors. Moreover, similar behaviors on cooperation could be found in two-layer random networks.展开更多
基金Supported by the New Century Excellent Talent Project of the Ministry of Education of China under Grant No NECT-07-0112, and the National Natural Science Foundation of China under Grant No 10775022.
基金Supported by the New Century Excellent Talent Project of the Ministry of Education of China under Grant No NECT-07-0112, the National Natural Science Foundation of China under Grant No 10775022, and the Fundamental Research Funds for the Central Universities （BUPT2009CZ02）.
文摘We focus on the effects of individuals＇ degrees on spontaneous cooperation. By investigating evolutionary PDGs on random networks with two distinct degrees, we find some resonance-type behaviors of the cooperator frequency with the variation of degree. We also find that increasing hums degree actually disfavors the cooperation though the heterogeneity in degree can enhance cooperation in the population.
基金Supported by the New Century Excellent Talent Project （NCET） of the Ministry of Education of China under Grant No NECT-07-0112, THE National Natural Science Foundation of China under Grant No 10775022, and the Fundamental Research Funds for the Central Universities.
基金Supported by the New Century Excellent Talent Project of the Ministry of Education of China under Grant No NECT-07-0112, the National Natural Science Foundation of China under Grant No 10775022, and the Fundamental Research Funds for the Central Universities
基金Supported by the National Natural Science Foundation of China under Grant Nos 71301012 and A050105
文摘The Ott-Antonsen ansatz provides a powerful tool in investigating synchronization among coupled phase oscil- lators. However, previous works using the ansatz only focused on the evolution of the order parameter and the information on desynchronized oscillators is less discussed. In this work, we show that the Ott-Antonsen ansatz can also be applied to investigate the desynchronous dynamics in coupled phase oscillators. Studying the original Kuramoto model and two of its variants, we find that the dynamics of α（ω）, the coefficient in the Fourier series of the probability density, can give most of the information on the synchronization, for example, the threshold of natural frequency delimiting the oscillators synchronized and desychronized by the mean field, the formulation of the effective frequency ωe （ω） of desynchronous oscillators, and the structure of the graph ωe （ω）.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10775022, 90921015the Fundamental Research Funds for the Central Universities
文摘We investigate the evolutionary prisoner’s dilemma game in structured populations by introducing dimers,which are defined as that two players in each dimer always hold a same strategy.We find that influences of dimerson cooperation depend on the type of dimers and the population structure.For those dimers in which players interactwith each other,the cooperation level increases with the number of dimers though the cooperation improvement leveldepends on the type of network structures.On the other hand,the dimers,in which there are not mutual interactions,will not do any good to the cooperation level in a single community,but interestingly,will improve the cooperationlevel in a population with two communities.We explore the relationship between dimers and self-interactions and findthat the effects of dimers are similar to that of self-interactions.Also,we find that the dimers,which are establishedover two communities in a multi-community network,act as one type of interaction through which information betweencommunities is communicated by the requirement that two players in a dimer hold a same strategy.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11575036,71301012,and 11505016
文摘We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner＇s dilemma game （PDG） in one layer and snowdrift game （SDG） in the other. We explore the dependences of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer. Moreover, in contrast to the result for PDG in single-layer square lattices, the parameter regime where cooperation could be maintained expands significantly in the PDG layer. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors. Moreover, similar behaviors on cooperation could be found in two-layer random networks.
