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We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…
We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…
Synchronization is a ubiquitous phenomenon in nature. Although it is necessary for the functioning of many systems, too much synchronization can also be detrimental, e.g., (partially) synchronized brain patterns support high-level cognitive…
The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter, we demonstrate that the nodes in a second-order Kuramoto model, perform a cascade…
A new collective behavior of resonant synchronization is discovered and the ability to retrieve information from brain memory is proposed based on this mechanism. We use modified Kuramoto phase oscillator to simulate the dynamics of a…
Dynamics of complex systems are often driven by interactions that extend beyond pairwise links, underscoring the need to establish a correspondence between interpretable system parameters and emergent phenomena in hypergraph-based networks.…
We study the bifurcations and phase diagram for a network of identical Kuramoto oscillators with a coupling that explicitly breaks the rotational symmetry of the equations. Applying the Watanabe-Strogatz ansatz, the original N-dimensional…
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…
In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…
The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…
Real-world networks are often characterized by simultaneous interactions between multiple agents that adapt themselves due to feedback from the environment. In this article, we investigate the dynamics of an adaptive multilayer network of…
The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…
Synchronization processes are ubiquitous despite the many connectivity patterns that complex systems can show. Usually, the emergence of synchrony is a macroscopic observable, however, the microscopic details of the system, as e.g. the…
Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…
We study a system of coupled oscillators of the Sakaguchi-Kuramoto type with interactions including a phase delay. We consider the case of a coupling matrix such that oscillators with large natural frequencies drive all slower ones but not…
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…
We study a generalized Kuramoto model in which each oscillator carries two coupled phase variables, representing a minimal swarmalator system. Assuming perfect correlation between the intrinsic frequencies associated with each phase…
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such…