Related papers: Interfaces with internal structures in generalized…
We construct and study a discrete time model describing the conflict interaction between two complex systems with non-trivial internal structures. The external conflict interaction is based on the model of alternative interaction between a…
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 obvious winner, but cyclic dominance is also at the heart…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
We consider systems with two competing species whose actions are completely symmetric, with same mobility, reproduction and competition rates. Numerical implementations of the model in two and three-dimensional space show that regions of…
We show that spatial models of simple predator-prey interactions predict that predator and prey numbers oscillate in time and space. These oscillations are not seen in the deterministic versions of the models, but are due to stochastic…
In this work we study the behavior of classical two-person, two-strategies evolutionary games on networks embedded in a Euclidean two-dimensional space with different kinds of degree distributions and topologies going from regular to…
Models of strategy evolution on static networks help us understand how population structure can promote the spread of traits like cooperation. One key mechanism is the formation of altruistic spatial clusters, where neighbors of a…
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for…
Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the…
We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the…
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium…
The spatio-temporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatio-temporal patterns arising from the cyclic competition between…
Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…
If one isolated species (corporation) is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species (corporations) can be expressed by a coupled system of two discrete logistic…
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…
The spatial segregation of species is fundamental to ecosystem formation and stability. Behavioural strategies may determine where species are located and how their interactions change the local environment arrangement. In response to…
Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
Cyclic predator-prey systems have been shown to give rise to rich, and novel, space-time patterns, as for example coarsening domains with non-trivial in-domain dynamics. In this work we study numerically the responses of a cyclic…