Related papers: Metastability induced by non-reciprocal adaptive c…
We investigate a network of integrate-and-fire neurons characterized by a distribution of spiking frequencies. Upon increasing the coupling strength, the model exhibits a transition from an asynchronous regime to a nontrivial collective…
We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
All the fundamental interactions (such as gravity or electromagnetic interactions) are reciprocal in nature. However, in the macroscopic world, in particular outside equilibrium, non-reciprocal or non-mutual interactions are quite…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent…
One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
In a large variety of systems (biological, physical, social etc.), synchronization occurs when different oscillating objects tune their rhythm when they interact with each other. The different underlying network defining the connectivity…
Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
In this PhD thesis, we study topological defects in two-dimensional non-equilibrium systems, focusing on active extensions of the XY model, including activity, mobility and non-reciprocity. In a noisy Kuramoto lattice with short-range…
Meta-stable states are identified in the Ising model with competition between the Glauber and Kawasaki dynamics. The model of interaction between magnetic moments was implemented on a network where the degree distribution follows a…
Most studies of collective phenomena in oscillator networks focus on directly coupled systems as exemplified by the classical Kuramoto model. However, there are growing number of examples in which oscillators interact indirectly via a…
The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions…
Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our…
The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like…
We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase…