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There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
We propose here a multiplex network approach to investigate simultaneously different types of dependency in complex data sets. In particular, we consider multiplex networks made of four layers corresponding respectively to linear,…
We present two models of sparse dynamic networks that display transitivity - the tendency for vertices sharing a common neighbour to be neighbours of one another. Our first network is a continuous time Markov chain $G=\{G_t=(V,E_t), t\ge…
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…
This paper models stochastic process of price time series of CSI 300 index in Chinese financial market, analyzes volatility characteristics of intraday high-frequency price data. In the new generalized Barndorff-Nielsen and Shephard model,…
A class of dynamic threshold models is proposed, for describing the upset of collective actions in social networks. The agents of the network have to decide whether to undertake a certain action or not. They make their decision by comparing…
We propose some kinetic models of wealth exchange and investigate their behavior on directed networks though numerical simulations. We observe that network topology and directedness yields a variety of interesting features in these models.…
We study the time dependence of maximal spanning trees and asset graphs based on correlation matrices of stock returns. In these networks the nodes represent companies and links are related to the correlation coefficients between them.…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
We study the dynamical properties of a finite dynamical network composed of two interacting populations, namely; extrovert ($a$) and introvert ($b$). In our model, each group is characterized by its size ($N_a$ and $N_b$) and preferred…
We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing…
We consider the population dynamics of a set of species whose network of catalytic interactions is described by a directed graph. The relationship between the attractors of this dynamics and the underlying graph theoretic structures like…
Many real-world social networks constantly change their global properties over time, such as the number of edges, size and density. While temporal and local properties of social networks have been extensively studied, the origin of their…
We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions, as well as degree correlations (assortativity).…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of…