Related papers: Insights into oscillator network dynamics using a …
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states…
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…
Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator…
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In…
This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…
We propose a set of general coupling conditions to select a coupling profile (a set of coupling matrices) from the linear flow matrix (LFM) of dynamical systems for realizing global stability of complete synchronization (CS) in identical…
We propose a theoretical framework to study the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to understand synchronization phenomena in networks of interneurons which possess…
This letter concerns the reliability of coupled oscillator networks in response to fluctuating inputs. Reliability means that (following a transient) an input elicits identical responses upon repeated presentations, regardless of the…
For a system of coupled identical phase oscillators with full permutation symmetry, any broken symmetries in dynamical behaviour must come from spontaneous symmetry breaking, i.e. from the nonlinear dynamics of the system. The dynamics of…
We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e.,…
We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf…
We investigate the existence of an optimal interplay between the natural frequencies of a group chaotic oscillators and the topological properties of the network they are embedded in. We identify the conditions for achieving phase…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…