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Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…

We review some of the recent literature, including Refs. [1-3], on the effects of non-normality on the synchronization of networks of oscillators, and provide numerical evidence that the basin of attraction about the synchronous solution is…

In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…

In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…

Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection…

We study the emergence of synchronisation in a chiral network of harmonic oscillators. The network consists of a set of locally incoherently pumped harmonic oscillators coupled pairwise in cascade with travelling field modes. Such cascaded…

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…

Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…

We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…

A central mechanism of linearised two dimensional shear instability can be described in terms of a nonlinear, action-at-a-distance, phase-locking resonance between two vorticity waves which propagate counter to their local mean flow as well…

An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context,…

We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…

The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…

We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…

A procedure is developed and tested to enforce synchronicity in a family of Stuart-Landau oscillators, coupled through a symmetric network. The proposed method exploits network plasticity, as an inherent non autonomous drive. More…

We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…

We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…

A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…

We study the global synchronization of hierarchically-organized Stuart-Landau oscillators, where each subsystem consists of three oscillators with activity-dependent couplings. We consider all possible coupling signs between the three…

Starting with an initial random network of oscillators with a heterogeneous frequency distribution, its autonomous synchronization ability can be largely improved by appropriately rewiring the links between the elements. Ensembles of…