Related papers: Basin sizes depend on stable eigenvalues in the Ku…
Synchronization is observed in many natural systems, with examples ranging from neuronal activation to walking pedestrians. The models proposed by Winfree and Kuramoto stand as the classic frameworks for investigating these phenomena. The…
We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and…
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…
We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the…
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two…
Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto…
Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramoto's results and obtain a mathematical…
Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. In this study, we develop methods to optimize the synchronization stability of the Kuramoto model by minimizing the…
Understanding how higher-order interactions shape the energy landscape of coupled oscillator networks is crucial for characterizing complex synchronization phenomena. Here, we investigate a generalized Kuramoto model with triadic…
The statistical properties of the Salerno model is investigated. In particular, a comparison between the coherent and partially coherent wave modes is made for the case of a random phased wave packet. It is found that the random phased…
We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies…
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the…
Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a…
The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase reduction to an ensemble of heterogeneous,…
We study the Kuramoto model (KM) having random natural frequencies and defined on uniform graphs that may be complete, random dense or random sparse. The natural frequencies are assumed to be independent and identically distributed on a…
We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can…
To study the manifestation of the Aharonov-Bohm effect in many-body systems we consider the statistical mechanics of the Gross-Neveu model on a ring (1+1 dimensions) and on a cylinder (2+1 dimensions) with a thin solenoid coinciding with…
We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian Mean Field model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi…
We consider a variation of the Kuramoto model with dynamic coupling, where the coupling strengths are allowed to evolve in response to the phase difference between the oscillators, a model first considered by Ha, Noh and Park. In particular…
Over the past decades chimera states have attracted considerable attention given their unexpected symmetry-breaking spatio-temporal nature, simultaneously exhibiting synchronous and incoherent behaviours under specific conditions. Despite…