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Many biological, technological, and social systems can be effectively described as networks of interacting subsystems. Typically, these networks are not isolated objects, but interact with their environment through both signals and…
Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
Evaluating a neural network on an input that differs markedly from the training data might cause erratic and flawed predictions. We study a method that judges the unusualness of an input by evaluating its informative content compared to the…
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…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the…
We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the…
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…
Networks are useful descriptions of the structure of many complex systems. Unsurprisingly, it is thus important to analyze the robustness of networks in many scientific disciplines. In applications in communication, logistics, finance,…
We introduce a model of adaptive temporal networks whose evolution is regulated by an interplay between node activity and dynamic exchange of information through links. We study the model by using a master equation approach. Starting from a…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…
Many observables of brain dynamics appear to be optimized for computation. Which connectivity structures underlie this fine-tuning? We propose that many of these structures are naturally encoded in the space that more directly relates to…
Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…
Networks built to model real world phenomena are characeterised by some properties that have attracted the attention of the scientific community: (i) they are organised according to community structure and (ii) their structure evolves with…
The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…