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We consider the quantum dynamics of a pair of coupled quantum oscillators coupled to a common correlated dissipative environment. The resulting equations of motion for both the operator moments and covariances can be integrated analytically…

We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the…

We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with…

An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…

This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the…

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now…

This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…

We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…

Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a…

We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…

We study a chain of $N+1$ phase oscillators with asymmetric but uniform coupling. This type of chain possesses $2^{N}$ ways to synchronize in so-called travelling wave states, i.e. states where the phases of the single oscillators are in…

We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a…

The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…

This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…

We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…

In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a…

We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We…

We consider here the dynamics of some homogeneous and isotropic cosmological models with $N$ interacting classical scalar fields non-minimally coupled to the spacetime curvature, as an attempt to generalize some recent results obtained for…

This paper studies the global feedback stabilization problem of a system with two pistons and the area between them containing a viscous compressible fluid (gas) modeled by the Navier-Stokes equations. The control input is the force applied…

For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system…