相关论文: Nonlinear Dynamics of the Rock-Paper-Scissors Game…
We explore a replicator-mutator model of the repeated Prisoner's Dilemma involving three strategies: always cooperate (ALLC), always defect (ALLD), and tit-for-tat (TFT). The dynamics resulting from single unidirectional mutations are…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be…
In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…
Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics.…
We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a…
Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD)…
We study a system of self-propelled, proliferating finite-size disks with game-theoretical interactions, where growth rates depend on local population composition. We analyze how these interactions influence spatial distribution,…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…
We investigate the adaptive Ambush strategy in cyclic models following the rules of the spatial rock-paper-scissors game. In our model, individuals of one species possess cognitive abilities to perceive environmental cues and assess the…
The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose…
Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the…
Evolutionary game theory has traditionally assumed that all individuals in a population interact with each other between reproduction events. We show that eliminating this restriction by explicitly considering the time scales of interaction…
In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise non-overlapping unstructured population of individuals mating at random. Our main finding…
We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…
We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include…
We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We…
Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…