Related papers: Dynamic fractals in spatial evolutionary games
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
We simulate binary soft disk systems in two dimensions, and investigate how the dynamics slow as the area fraction is increased toward the glass transition. The "fragility" quantifies how sensitively the relaxation time scale depends on the…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this…
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…
We show that critical systems of finite size develop a fractal structure in momentum space with anomalous dimension given in terms of the isotherm critical exponent delta of the corresponding infinite system. The associated power laws of…
Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system…
Cooperative behavior lies at the very basis of human societies, yet its evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
We present a detailed study of prisoner's dilemma game with stochastic modifications on a two-dimensional lattice, in presence of evolutionary dynamics. By very nature of the rules, the cooperators have incentive to cheat and the fear to…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
We consider a stochastic Laplacian growth problem in the framework of normal random matrices. In the large $N$ limit the support of eigenvalues of random matrices is a planar domain with a sharp boundary which evolves under a change in the…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
A simple model of macroevolution is proposed exhibiting both the property of punctuated equilibrium and the dynamics of potentialities for different species to evolve towards increasingly higher complexity. It is based on the phenomenon of…
Dynamical evolution plays a key role in shaping the current properties of star clusters and star cluster systems. A detailed understanding of the effects of evolutionary processes is essential to be able to disentangle the properties which…
One of the most striking effect of fluctuations in evolutionary game theory is the possibility for mutants to fixate (take over) an entire population. Here, we generalize a recent WKB-based theory to study fixation in evolutionary games…
Players of coevolutionary games may update not only their strategies but also their networks of interaction. Based on interpreting the payoff of players as fitness, dynamic landscape models are proposed. The modeling procedure is carried…
Spatial evolutionary games are studied with myopic players whose payoff interest, as a personal character, is tuned from selfishness to other-regarding preference via fraternity. The players are located on a square lattice and collect…
A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely…
A frequently encountered situation in the study of delay systems is that the length of the delay time changes with time, which is of relevance in many fields such as optics, mechanical machining, biology or physiology. A characteristic…