Related papers: Dynamic fractals in spatial evolutionary games
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly-plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random…
Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering…
Coevolutionary games cast players that may change their strategies as well as their networks of interaction. In this paper a framework is introduced for describing coevolutionary game dynamics by landscape models. It is shown that…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding…
The fractal dimension of excitations in glassy systems gives information on the critical dimension at which the droplet picture of spin glasses changes to a description based on replica symmetry breaking where the interfaces are space…
I present a simplified analytical model that simulates the evolution of the binary population in a dynamically evolving globular cluster. A number of simulations have been run spanning a wide range in initial cluster and environmental…
Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the…
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…
We study numerically the spatial properties of relaxation clusters in a two dimensional sandpile automaton with dynamic rules depending stochastically on a parameter p, which models the effects of static friction. In the limiting cases p=1…
The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid…
We raise the hypothesis that the density fluctuations field which originates the growth of large scale structures is a combination of two or more distributions. By applying the statistical analysis of finite mixture distributions to a…
We study a spatial, one-shot prisoner's dilemma (PD) model in which selection operates on both an organism's behavioral strategy (cooperate or defect) and its choice of when to implement that strategy across a set of discrete time slots.…
Dynamics of coarsening of a statistically homogeneous fractal cluster, created by a morphological instability of diffusion-controlled growth, is investigated theoretically. An exact mathematical setting of the problem is presented that…
The evolution of marginally bound supercluster-like objects in an accelerating LambdaCDM Universe is followed, by means of cosmological simulations, from the present time to an expansion factor a = 100. The objects are identified on the…
We present a Monte Carlo study of the fractal geometry of clusters formed by discrete-time simple random walks (sRW) of $L^2$ steps on a periodic square $L\times L$ lattice. We verify with high precision that the asymptotic behavior of the…
We introduce an analytical model to study the evolution towards equilibrium in spatial games, with `memory-aware' agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner's…
Dynamics of ordering in Ising model, following quench to zero temperature, have been studied via Glauber spin-flip Monte Carlo simulations in space dimensions $d=2$ and $3$. One of the primary objectives has been to understand phenomena…