Evolutionary games and spatial periodicity

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.

Renewal of Urban Industrial Zone and Spatial Game in China:A Case Study of Chengdu Eastern Suburb Industrial Zone

The change of system constantly reshapes the urban form of China after 1949,among which the renewal and transformation of industrial zones is a typical phenomenon in the changing process of urban landscape in recent years,which centrally refl ects the development characteristics of contemporary Chinese cities under new social background.From the perspective of spatial game,this paper takes Chengdu Eastern Suburb Industrial Zone as an example,studies and interprets the changes of urban form and the causes of these changes in the renewal process of the industrial zone on the basis of the existing morphological frame and material landscapes,so then shows the particularity and complexity of the process of urban spatial reconstruction with current Chinese characteristics.

Influence of Strategy Continuity on Cooperation in Spatial Prisoner’s Dilemma Games with Migrating Players

The phenomenon of cooperation is prevalent in both nature and human society. In this paper a simulative model is developed to examine how the strategy continuity influences cooperation in the spatial prisoner＇s games in which the players migrate through the success-driven migration mechanism. Numerical simulations illustrate that the strategy continuity promotes cooperation at a low rate of migration, while impeding cooperation when the migration rate is higher. The influence of strategy continuity is also dependent on the game types. Through a more dynamic analysis, the different effects of the strategy continuity at low and high rates of migration are explained by the formation, expansion, and extinction of the self-assembled clusters of ＂partial-cooperators＂ within the gaming population.

Species diversity in rock–paper–scissors game coupling with Levy flight

The rock–paper–scissors （RPS） game is a nice model to study the biodiversity in an ecosystem. However, in the previous studies only the nearest-neighbor interaction among the species was considered. In this paper, taking the long-range migration into account, the effects of the interplay between nearest-neighbor-interaction and long-range-interaction given by Levy flight with distance distribution lh （-3 ≤ h 〈-1） in the spatial RPS game are investigated. Taking the probability, exchange rate, and power-law exponent of Levy flight as parameters, the coexistence conditions of three species are given. The critical curves for stable coexistence of three species in the parameter space are presented. It is also found that Levy flight has interesting effects on the final spatiotemporal pattern of the system. The results reveal that the long-range-interaction given by Levy flight exhibits pronounced effects on biodiversity of the ecosystem.