Related papers: Order parameter analysis of synchronization transi…
We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart-Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation…
The celebrated Ott-Antonsen ansatz for coupled oscillators provides a useful framework to work with deterministic systems in the thermodynamic limit, but remains just an approximation for stochastic models. In this paper, I construct a…
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…
Phase resetting curves characterize the way a system with a collective periodic behavior responds to perturbations. We consider globally coupled ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of ensemble…
We study the dynamics of a generalized version of the famous Kuramoto-Sakaguchi coupled oscillator model. In the classic version of this system, all oscillators are governed by the same ODE, which depends on the order parameter of the…
We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
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.,…
Understanding how large complex networks achieve synchronization is a problem of fundamental interest, and is typically studied in the asymptotic steady-state regime. In contrast, this study investigates how higher-order interactions affect…
The framework of mutually coupled oscillators on a network has served as a convenient tool for investigating the impact of various parameters on the dynamics of real-world systems. Compared to large networks of oscillators, minimal networks…
We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…
We study the effects of phase-frustrated, higher-order interactions in a system of coupled phase oscillators with two communities. We use dimensionality reduction techniques to derive a low-dimensional system of ODEs to describe the…
Watanabe-Strogatz theory provides a low-dimensional description of identical Kuramoto oscillators via the framework of the M\"obius transformation. Here, using the Watanabe-Strogatz theory, we provide a unifying description for a broad…
This work analyzes the problem of community structure in real-world networks based on the synchronization of nonidentical coupled chaotic R\"{o}ssler oscillators each one characterized by a defined natural frequency, and coupled according…
We investigate the phase diagram of the Sakaguchi-Kuramoto model with a higher order interaction along with the traditional pairwise interaction. We also introduce asymmetry parameters in both the interaction terms and investigate the…
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…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
We investigate the network model of community by Watts, Dodds and Newman (D. J. Watts et al., Science 296 (2002) 1302) as a hierarchy of groups, each of 5 individuals. A homophily parameter $\alpha$ controls the probability proportional to…