Related papers: Long range action in networks of chaotic elements
We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
Nonextensivity is foreseeable in network ensembles, as heterogeneous interactions generally exist in complex networked systems that need to be described by network ensembles. But this nonextensivity has not been literatured proved yet. In…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
We reduce complex stripped patterns to a basic topological network of edges and vertices to define defects and measure their influence on the pattern. We present statistics on the spatial and temporal distribution of defects within the…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
We present a chemical reaction network that is unstable under deterministic mass action kinetics, exhibiting finite-time blow-up of trajectories in the interior of the state space, but whose stochastic counterpart is positive recurrent.…
Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
Long range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics.…
We consider critical phenomena on heterogeneous small-world networks having a scale-free character but also arbitrary short-loops. After deriving the self-consistent equation for the order parameter and the critical surface, we prove that…
We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…