Spatial interactions are considered an important factor influencing a variety of evolutionary processes that take place in structured populations.It still remains an open problem to fully understand evolutionary game ...Spatial interactions are considered an important factor influencing a variety of evolutionary processes that take place in structured populations.It still remains an open problem to fully understand evolutionary game dynamics on networks except for certain limiting scenarios such as weak selection.Here we study the evolutionary dynamics of spatial games under strong selection where strategy evolution of individuals becomes deterministic in a fashion of winners taking all.We show that the long term behavior of the evolutionary process eventually converges to a particular basin of attraction,which is either a periodic cycle or a single fixed state depending on specific initial conditions and model parameters.In particular,we find that symmetric starting configurations can induce an exceedingly long transient phase encompassing a large number of aesthetic spatial patterns including the prominent kaleidoscopic cooperation.Our finding holds for any population structure and a broad class of finite games beyond the Prisoner’s Dilemma.Our work offers insights into understanding evolutionary dynamics of spatially extended systems ubiquitous in biology and ecology.展开更多
Women have made steady gains in project management on many fronts including participation and compensation.On compensation,the gap between men and women has steadily decreased from 24%in 1996 to 18%in 2000;in the late...Women have made steady gains in project management on many fronts including participation and compensation.On compensation,the gap between men and women has steadily decreased from 24%in 1996 to 18%in 2000;in the latest Project Management Institute(PMI)global salary survey in late 2017,the gap is now nearly 14%(with variations in different regions as seen in Table 1).However,more must be done to attract women to展开更多
基金support from NSFC,China(62036002,62273226)is gratefully acknowledgedsupported by the Fundamental Research Funds for Central Universities,Xidian University,China(JB210414).
文摘Spatial interactions are considered an important factor influencing a variety of evolutionary processes that take place in structured populations.It still remains an open problem to fully understand evolutionary game dynamics on networks except for certain limiting scenarios such as weak selection.Here we study the evolutionary dynamics of spatial games under strong selection where strategy evolution of individuals becomes deterministic in a fashion of winners taking all.We show that the long term behavior of the evolutionary process eventually converges to a particular basin of attraction,which is either a periodic cycle or a single fixed state depending on specific initial conditions and model parameters.In particular,we find that symmetric starting configurations can induce an exceedingly long transient phase encompassing a large number of aesthetic spatial patterns including the prominent kaleidoscopic cooperation.Our finding holds for any population structure and a broad class of finite games beyond the Prisoner’s Dilemma.Our work offers insights into understanding evolutionary dynamics of spatially extended systems ubiquitous in biology and ecology.
文摘Women have made steady gains in project management on many fronts including participation and compensation.On compensation,the gap between men and women has steadily decreased from 24%in 1996 to 18%in 2000;in the latest Project Management Institute(PMI)global salary survey in late 2017,the gap is now nearly 14%(with variations in different regions as seen in Table 1).However,more must be done to attract women to
