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 …

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 …

In a diverse population, where many species are present, competitors can fight for surviving
at individual and collective levels. In particular, species, which would beat each other …

We study a class of the stochastic May-Leonard models, with three species dominating each
other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We …

Recognizing territories is essential to decide behavior of population either human or
animals, and interaction between groups or individuals according to the territorial …

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 …

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 …

In ecosystems, cooperative behavior is universal and can dramatically improve a species'
chances of survival. Nevertheless, the situations that can occur when different species with …

The self-protection of alliances against external invaders is a key concept behind the
maintenance of biodiversity in the face of natural selection. But since these alliances, which …