Related papers: Continuum limit for interacting systems on adaptiv…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely…
In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial…
We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the…
A recurrent idea in the study of complex systems is that optimal information processing is to be found near bifurcation points or phase transitions. However, this heuristic hypothesis has few (if any) concrete realizations where a standard…
We consider a system of $N$ particles whose interactions are characterized by a (weighted) graph $G^N$. Each particle is a node of the graph with an internal state. The state changes according to Markovian dynamics that depend on the states…
People organize in groups and contagions spread across them. A simple process, but complex to model due to dynamical correlations within groups and between groups. Groups can also change as agents join and leave them to avoid infection. To…
We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on…
In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
We study information processing in populations of Boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
This article studies the synchronization problem of complex dynamical networks. The impulsive control method is considered with a novel event-triggered pinning algorithm. Sufficient conditions on the network topology are obtained to ensure…
Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization…
Fokker-Planck equations represent a suitable description of the finite-time behavior for a large class of particle systems as the size of the population tends to infinity. Recently, the theory of graph limits has been introduced in the…