Related papers: Extremal dynamics model on evolving networks

Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks…

A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond.…

When there is no independence, abnormal observations may have a tendency to appear in clusters instead of scattered along the time frame. Identifying clusters and estimating their size are important problems arising in statistics of…

By driven to extinction species less or poorly adapted, the Darwinian evolutionary theory is intrinsically an optimization theory. We investigate two optimization algorithms with such evolutionary characteristics: the Bak-Sneppen and the…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…

We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

In common descriptions of phase transitions, first order transitions are characterized by discontinuous jumps in the order parameter and normal fluctuations, while second order transitions are associated with no jumps and anomalous…

In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…

Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the…

We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important…

We study how the community structure of bipartite mutualistic networks changes in a dynamic context. First, we consider a real mutualistic network and introduce extinction events according to several scenarios. We model extinctions as node…

It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…

We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great…

We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…

We study the avalanche dynamics in the data packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with a proportionality constant $1+a$. When the system is…

A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…

The co-authorship network of scientists represents a prototype of complex evolving networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an eight-year period (1991-98), we infer…

By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…