Related papers: Synchronization of Weakly Coupled Oscillators: Cou…
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions---subsets of the phase space filled…
A long-standing expectation is that two repulsively coupled oscillators tend to oscillate in opposite directions. It has been difficult to achieve complete synchrony in coupled identical oscillators with purely repulsive coupling. Here, we…
Synchronization in quantum systems has been recently studied through persistent oscillations of local observables, which stem from undamped modes of the dissipative dynamics. However, the existence of such modes requires fine-tuning the…
The synchronization of coupled organ pipes represents a nonlinear phenomenon with significant implications for both musical acoustics and nonlinear dynamics. This study investigates the coupling mechanisms governing synchronization,…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
We study the existence and stability of synchronous solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter…
We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of…
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…
We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate…
We investigate a system of four nearest neighbour bidirectional coupled phase oscillators of dissimilar initial frequencies in a ring at the changeover into a synchronizing state. There are twenty four permutations upon assigning the…
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behaviour through a change of stability…
Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…
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…
While shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network,the suppressing tendency of the heterogeneity of the degree distribution, even for…
This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of…
Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the transient…
Previous research on nonlinear oscillator networks has shown that chaos synchronization is attainable for identical oscillators but deteriorates in the presence of parameter mismatches. Here, we identify regimes for which the opposite…
Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently…