Related papers: Functional role of synchronization: A mean-field c…
We investigate team optimal control of stochastic subsystems that are weakly coupled in dynamics (through the mean-field of the system) and are arbitrary coupled in the cost. The controller of each subsystem observes its local state and the…
From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…
We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…
Electrical synapses play a major role in setting up neuronal synchronization, but the precise mechanisms whereby these synapses contribute to synchrony are subtle and remain elusive. To investigate these mechanisms mean-field theories for…
Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled objects in interaction. Though these models are much simpler than the underlying differential games they describe in some limit, their…
Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…
In this paper, we investigate team optimal control of coupled major-minor subsystems with mean-field sharing. In such a model, there is one major subsystem that directly influences the dynamics of $n$ homogeneous minor subsystems; however,…
Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains,…
This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…
This paper gives a fresh look at network synchronization. Here we no longer analyze it from the view of mathematics, such as graph theory, while we probe into one from control theory. First, we analyze the synchronization region using the…
Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
We consider network aggregative games to model and study multi-agent populations in which each rational agent is influenced by the aggregate behavior of its neighbors, as specified by an underlying network. Specifically, we examine systems…
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent…
Synchronization phenomena are pervasive in biology. In neuronal networks, the mechanisms of synchronization have been extensively studied from both physiological and computational viewpoints. The functional role of synchronization has also…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
Spontaneous synchronization is a general phenomenon in which a large population of coupled oscillators of diverse natural frequencies self-organize to operate in unison. The phenomenon occurs in physical and biological systems over a wide…
We establish a connection between federated learning, a concept from machine learning, and mean-field games, a concept from game theory and control theory. In this analogy, the local federated learners are considered as the players and the…