Related papers: Balanced Dynamics in Strongly Coupled Networks
Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers…
When brain signals are recorded in an electroencephalogram or some similar large-scale record of brain activity, oscillatory patterns are typically observed that are thought to reflect the aggregate electrical activity of the underlying…
Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
This paper addresses the behavior analysis problems for directed signed networks that involve cooperative-antagonistic interactions among agents. Of particular interest is to explore the convergence behaviors of directed signed networks…
Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present…
Many studies have shown that the excitation and inhibition received by cortical neurons remain roughly balanced across many conditions. A key question for understanding the dynamical regime of cortex is the nature of this balancing.…
The paper is devoted to the approximate consensus problem for networks of nonlinear agents with switching topology, noisy and delayed measurements. In contrast to the existing stochastic approximation-based control algorithms (protocols), a…
The activity of neurons is correlated, and this correlation affects how the brain processes information. We study the neural circuit mechanisms of correlations by analyzing a network model characterized by strong and heterogeneous…
Biological neural networks face a formidable task: performing reliable computations in the face of intrinsic stochasticity in individual neurons, imprecisely specified synaptic connectivity, and nonnegligible delays in synaptic…
This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These…
In this paper, we propose a general mathematical framework to represent many multi-agent signalling systems in recent works. Our goal is to apply previous results in monotonicity to this class of systems and study their asymptotic behavior.…
Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…
In this work, we consider a multi-population system where the dynamics of each agent evolve according to a system of stochastic differential equations in a general functional setup, determined by the global state of the system. Each agent…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
For a multi-agent system state estimation resting upon noisy measurements constitutes a problem related to several application scenarios. Adopting the standard least-squares approach, in this work we derive both the (centralized) analytic…
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…
We study a non-exchangeable multi-agent system and rigorously derive a strong form of the mean-field limit. The convergence of the connection weights and the initial data implies convergence of large-scale dynamics toward a deterministic…
We determine limiting equations for large asymmetric `spin glass' networks. The initial conditions are not assumed to be independent of the disordered connectivity: one of the main motivations for this is that allows one to understand how…