Related papers: Validity of numerical trajectories in the synchron…
Conditions such as insomnia, cardiac arrhythmia and jet-lag share a common feature: they are all related to the ability of biological systems to synchronize with the day-night cycle. When organisms lose resilience, this ability of…
The cooperative behavior of neurons and neuronal areas associated with the synchronization behavior proves to be a fundamental neural mechanism. In addition, abnormal levels of synchronization have been related to unhealthy neural…
In this thesis we study synchronization phenomena in natural and artificial coupled multi-component systems, applicable to the scalability of parallel discrete-event simulation for systems with asynchronous dynamics. We analyze the…
The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally-coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension…
We employ a quantum trajectory approach to characterize synchronization and phase-locking between open quantum systems in nonequilibrium steady states. We exemplify our proposal for the paradigmatic case of two quantum Van der Pol…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector…
A {\it shadow} is an exact solution to a chaotic system of equations that remains close to a numerically computed solution for a long time, ending in a {\it glitch}. We study the distribution of shadow durations at low dimension and how…
The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The highly influential chaotic hypothesis of Gallavotti and…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…
As a quantification of the main bottleneck to flow over a graph, the network property of conductance plays an important role in the process of synchronization of network-coupled dynamical systems. Diffusive coupling terms serve not only to…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the…
We report the nature of transitions from nonsynchronous to complete synchronization (CS) state in arrays of time-delay systems, where the systems are coupled with instantaneous diffusive coupling. We demonstrate that the transition to CS…
The dynamics of symmetry breaking is an important issue in many branches of physics including the real time onset of the Higgs-effect. In this thesis I examine the linear and non-linear evolution of different systems in the broken symmetric…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…
Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control,…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…