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Higher-order interaction networks are typically modeled using hypergraphs or simplicial complexes, where interactions explicitly involve more than two nodes. Here we demonstrate that effective higher-order dynamical constraints emerge…
Phase locking experiments on vortex based spin transfer oscillators with an external microwave current are performed. We present clear evidence of phase locking, frequency pulling, as well as fractional synchronization in this system, with…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
A fundamental understanding of synchronized behavior in multi-agent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under…
We consider chimera states of coupled identical phase oscillators where some oscillators are phase synchronized while others are desynchronized. It is known that chimera states of non-locally coupled Kuramoto--Sakaguchi oscillators in…
The theory of cointegration has been a leading theory in econometrics with powerful applications to macroeconomics during the last decades. On the other hand the theory of phase synchronization for weakly coupled complex oscillators has…
Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to total synchronization. We are able to develop exact solutions for…
We study the onset of synchronization in square lattices of limit cycle oscillators with long-range coupling by means of numerical simulations of the Kuramoto model. In this regime the critical coupling strength depends on the system size…
Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rhythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards…
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…
We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different…
In a graph, we say that two nodes are topologically equivalent if their sets of first neighbors, excluding the two nodes, coincide. We prove that nonlinearly coupled heterogeneous oscillators located on a group of topologically equivalent…
Based on a local greedy numerical algorithm, we compute the topology of weighted, directed, and of unlimited extension networks of non identical Kuramoto oscillators which simultaneously satisfy 2 criteria: i) global frequency…
We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
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…
We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in…
We study the phase synchronization between collective rhythms of fully locked oscillator groups. For weakly interacting groups of two oscillators with global sinusoidal coupling, we analytically derive the collective phase coupling…
We study the efficiency of synchronization in ensembles of identical coupled stochastic oscillator systems. By deriving a chemical Langevin equation, we measure the rate at which the systems synchronize. The rate at which the difference in…
We suggest an adaptive control scheme for the control of zero-lag and cluster synchronization in delay-coupled networks. Based on the speed-gradient method, our scheme adapts the topology of a network such that the target state is realized.…