相关论文: Globally synchronized oscillations in complex cycl…

Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network,…

If rock beats scissors and scissors beat paper, one might assume that rock beats paper too. But this is not the case for intransitive relationships that make up the famous rock-paper-scissors game. However, the sole presence of paper might…

We study a spatial cyclic predator-prey model with an even number of species (for n=4, 6, and 8) that allows the formation of two defective alliances consisting of the even and odd label species. The species are distributed on the sites of…

Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…

Simulations of the coevolution of many interacting species are performed using the Webworld model. The model has a realistic set of predator-prey equations that describe the population dynamics of the species for any structure of the food…

Synchronization in a lattice of a finite population of phase oscillators with algebraically decaying, non-normalized coupling is studied by numerical simulations. A critical level of decay is found, below which full locking takes place if…

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 evolutionary game theory. In this work we assume that a…

We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…

Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…

Coherence evolution of two food web models can be obtained under the stirring effect of chaotic advection. Each food web model sustains a three--level trophic system composed of interacting predators, consumers and vegetation. These…

Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed…

One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described…

In a predator-prey metapopulation, the two traits are adversely related: synchronization and persistence. A decrease in synchrony apparently leads to an increase in persistence and, therefore, necessitates the study of desynchrony in a…

The rock-paper-scissors game is a model example of the on-going cyclic turnover typical of many ecosystems, ranging from the terrestrial and aquatic to the microbial. Here we explore the evolution of a rock-paper-scissors system where three…

We consider an example of cyclic competition bimatrix game which is a Rock-Scissors-Paper game with assumption about perfect memory of the playing agents. At first we investigate the dynamics in the neighbourhood of the Nash equilibrium as…

A theory of relative species abundance on sparsely-connected networks is presented by investigating the replicator dynamics with symmetric interactions. Sparseness of a network involves difficulty in analyzing the fixed points of the…

We study the network replicator equation and characterize its fixed points on arbitrary graph structures for $2 \times 2$ symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of…

We study diffusion on a multilayer network where the contact dynamics between the nodes is governed by a random process and where the waiting time distribution differs for edges from different layers. We study the impact on a random walk of…

We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations…

A coarse grained description of a two-dimensional prey-predator system is given in terms of a 3-state lattice model containing two control parameters: the spreading rates of preys and predators. The properties of the model are investigated…