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 …

Taxes are an essential and uniformly applied institution for maintaining modern societies.
However, the levels of taxation remain an intensive debate topic among citizens. If each …

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 …

We study generalised rock–paper–scissors models with an arbitrary odd number N≥ 5 of
species, among which n are weak, with 2≤ n≤(N− 1)/2. Because of the species' weakness …

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 …

Organisms may respond to local stimuli that benefit or threaten their fitness. The adaptive
movement behaviour may allow individuals to adjust their speed to maximise the chances of …

A balanced ecosystem with coexisting constituent species is often perturbed by different
natural events that persist only for a finite duration of time. What becomes important is …

The prototype of a cyclic dominant system is the so-called rock-scissors-paper game, but
similar relation among competing strategies can be identified in several other models of …

Sacrificing personal benefits for a common good is at odds with the fundamental principle of
Darwinian evolution: if only the fittest survives, then there should be no place for …

We investigate evolving dynamics of cyclically competing species on spatially extended
systems with considering a specific region, which is called the “wildlife refuge,” one of the …