Related papers: Higher-Order Network Interactions through Phase Re…
We study the conditions of amplitude death in a network of delay-coupled limit cycle oscillators by including time-varying delay in the coupling and self-feedback. By generalizing the master stability function formalism to include…
We propose a method for optimizing mutual coupling functions to achieve fast and global synchronization between a pair of weakly coupled limit-cycle oscillators. Our method is based on phase reduction that provides a concise low-dimensional…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
The importance of pulse-coupled oscillators (PCOs) in biology and engineering has motivated research to understand basic properties of PCO networks. Despite the large body of work addressing PCOs, a global synchronization result for…
Time-delayed oscillator networks underlie diverse biological and physical systems, yet standard first-order phase reductions fail to capture their high-dimensional collective dynamics. In this Letter, we develop a universal second-order…
Controlling the behavior of nonlinear systems on networks is a paramount task in control theory, in particular the control of synchronization, given its vast applicability. In this work, we focus on pinning control and we examine two…
The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
By a model of coupled phase oscillators, we show analytically how synchronization in {\em non-identical} complex networks can be enhanced by introducing a proper gradient into the couplings. It is found that, by pointing the gradient from…
Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to…
The effect of phase-lag parameter in pairwise interactions has been a topic of great interest for long. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We…
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…
Understanding the global dynamical behaviour of a network of coupled oscillators has been a topic of immense research in many fields of science and engineering. Various factors govern the resulting dynamical behaviour of such networks,…
Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real world applications, the…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
We introduce a generic model of weakly non-linear self-sustained oscillator as a simplified tool to study synchronisation in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of…
The Kuramoto-Sakaguchi model for coupled phase oscillators with phase-frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture…
The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a…
We study transition to phase synchronization in an ensemble of Stuart-Landau oscillators interacting on a star network. We observe that by introducing frequency weighted coupling and time scale variations in the dynamics of nodes, system…
We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and…