Related papers: Dynamical systems on ultra small-world networks
Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…
With improvements in data resolution and quality, researchers can now represent complex systems as signed, weighted, and directed networks. In this article, we introduce a framework for measuring net and indirect effects without simplifying…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…
Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
Classical approaches to ecological stability rely on fully connected interaction models, yet real ecosystems are sparse and structured--a feature that qualitatively reshapes their collective dynamics. Here, we establish a thermodynamically…
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…
If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…
The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from…
We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the…
In this paper, we introduce a general framework to quantify dissimilarities between generalized Lotka-Volterra dynamical processes, ranging from classical predator-prey systems to multispecies communities interacting on networks. The…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Real ecosystems are characterized by sparse and asymmetric interactions, posing a major challenge to theoretical analysis. We introduce a new method to study the generalized Lotka-Volterra model with stochastic dynamics on sparse graphs. By…