Related papers: Synchronization of Coupled Kuramoto Oscillators un…
We investigate the role of inertia in the asynchronous state of a disordered Kuramoto model. We extend an iterative simulation scheme to the case of the Kuramoto model with inertia in order to determine the self-consistent fluctuation…
Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that…
The Kuramoto model describes synchronization behavior among coupled oscillators and enjoys successful application in a wide variety of fields. Many of these applications seek phase-coherent solutions, i.e., equilibria of the model.…
Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal…
Higher-order networks with multiway interactions can exhibit collective dynamical phenomena that are absent in traditional pairwise network models. However, analyzing such dynamics becomes computationally prohibitive as their state space…
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…
While considerable progress has been made in the analysis of large systems containing a single type of coupled dynamical component (e.g., coupled oscillators or coupled switches), systems containing diverse components (e.g., both…
The Kuramoto model, a paradigmatic framework for studying synchronization, exhibits a transition to collective oscillations only above a critical coupling strength in the thermodynamic limit. However, real-world systems are finite, and…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…
In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is…
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,…
From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple…
The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…
We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…
We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…
We examine a modification of the Kuramoto model for phase oscillators coupled on a network. Here, two populations of oscillators are considered, each with different network topologies, internal and cross-network couplings and frequencies.…
The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make…
Motivated by recent observations in neuronal systems we investigate all-to-all networks of non-identical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all…
The mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed (by the method of multiple scales) near regions in its phase diagram corresponding to…
A knot is a circle embedded in the space. Projecting a knot on a plane, we obtain a diagram which is known as the knot diagram. The vertices of the diagram, where the curved lines are crossed, can be considered as sites occupied by…