Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This
simple game is popular among children and adults to decide on trivial disputes that have no …

Spatially extended population dynamics models that incorporate demographic noise serve
as case studies for the crucial role of fluctuations and correlations in biological systems …

Economic experiments have shown that punishment can increase public goods game
contributions over time. However, the effectiveness of punishment is challenged by second …

Lotka's seminal work (Lotka AJ, Proc. Natl. Acad. Sci. USA, 6 (1920) 410)" on certain
rhythmic relations" is already one hundred years old, but the research activity about pattern …

Complex systems in ecological science can be generally defined by either the number of
different species or the structure among species having many relations, and understanding …

Punishing those who refuse to participate in common efforts is a known and intensively
studied way to maintain cooperation among self-interested agents. But this act is costly …

Evolutionary dynamical models for cyclic competitions of three species (eg, rock, paper and
scissors, or RPS) provide a paradigm, at the microscopic level of individual interactions, to …

Game theory provides a general mathematical background to study the effect of pair
interactions and evolutionary rules on the macroscopic behavior of multi-player games …

Evolutionary games of cyclic competitions have been extensively studied to gain insights
into one of the most fundamental phenomena in nature: biodiversity that seems to be …

Competing strategies in an evolutionary game model, or species in a biosystem, can easily
form a larger unit which protects them from the invasion of an external actor. Such a …