Related papers: Evolutionary dynamics in the Bak-Sneppen model on …
Networks out of equilibrium display dynamics characterized by multiple equilibria and sudden transitions. These transitions arise when each node leaves its natural stable state and joins to an organized global activation behavior. In this…
The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
In considering a social network, there are cases where people is transferred to another place. Then the physical (direct) relations among nodes are lost by the movement. In terms of a network theory, some nodes break the present connections…
The Bak--Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value…
We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
We investigate dynamical systems characterized by a time series of distinct semi-stable activity patterns, as they are observed in cortical neural activity patterns. We propose and discuss a general mechanism allowing for an adiabatic…
Consider the following evolution model, proposed in \cite{BS} by Bak and Sneppen. Put $N$ vertices on a circle, spaced evenly. Each vertex represents a certain species. We associate with each vertex a random variable, representing the…
We investigate global stability and dynamics of large ecological networks by classical methods of the dynamical system theory, including Hamiltonian methods, and averaging. Our analysis exploits the network topological structure, namely,…
Nestedness characterizes the linkage pattern of networked systems, indicating the likelihood that a node is linked to the nodes linked to the nodes with larger degrees than it. Networks of mutualistic relationship between distinct groups of…
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
Small world models are networks consisting of many local links and fewer long range `shortcuts'. In this paper, we consider some particular instances, and rigorously investigate the distribution of their inter--point network distances. Our…
Evolutionary dynamics on graphs can lead to many interesting and counterintuitive findings. We study the Moran process, a discrete time birth-death process, that describes the invasion of a mutant type into a population of wild-type…
Links in a practical network may have different functions, which makes the original network a combination of some functional subnetworks. Here, by a model of coupled oscillators, we investigate how such functional subnetworks are evolved…
To understand the structural dynamics of a large-scale social, biological or technological network, it may be useful to discover behavioral roles representing the main connectivity patterns present over time. In this paper, we propose a…
We study the one-dimensional Bak-Sneppen model for the evolution of species in an ecosystem. Of particular interest are the temporal fluctuations in the fitness variables. We numerically compute the power spectral density and apply the…
We consider a multi-species community modelled as a complex network of populations, where the links are given by a random asymmetric matrix J, with fraction 1-C of zero entries, where C reflects the over-all connectivity of the system. The…