Related papers: Characterizing short-term stability for Boolean ne…
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…
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…
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…
For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…
Boolean networks, first developed in the late 1960s as a tool for studying complex disordered dynamical systems, consist of nodes governed by Boolean functions whose evolution is entirely deterministic in that the state of the network at a…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
In this paper we study disease spread over a randomly switched network, which is modeled by a stochastic switched differential equation based on the so called $N$-intertwined model for disease spread over static networks. Assuming that all…
In this paper we study networks of nodes characterised by binary traits that change both endogenously and through nearest-neighbour interaction. Our analytical results show that those traits can be ranked according to the noisiness of their…
Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current…
Propagation of balance-sheet or cash-flow insolvency across financial institutions may be modeled as a cascade process on a network representing their mutual exposures. We derive rigorous asymptotic results for the magnitude of contagion in…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
In this paper, we study estimation of potentially unstable linear dynamical systems when the observations are distributed over a network. We are interested in scenarios when the information exchange among the agents is restricted. In…
Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential…
Load balancing between adjacent base stations (BSs) is important for balancing load distributions and improving service provisioning. Whilst load balancing between any given pair of BSs is beneficial, cascade load sharing can cause network…
We evaluate the probability that a Boolean network returns to an attractor after perturbing h nodes. We find that the return probability as function of h can display a variety of different behaviours, which yields insights into the…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…