Running and Tumbling Localized Structures: A Non-Brownian Motion.

Macroscopic systems present particle-type solutions. Spontaneous symmetry-breaking can cause these solutions to travel in different directions, and the inclusion of random fluctuations can induce them to run and tumble. We investigate the running and tumbling of localized structures observed on a prototype model of one-dimensional pattern formation with noise.

The transition to synchronization of networked systems.

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network's nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained.

Endowing networks with desired symmetries and modular behavior.

Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a synthetical structure being furthermore perfectly reflected in the modular organization of the network's functioning. Our results solve a relevant problem of designing a desired set of clusters and are of generic application in all cases where a desired parallel functioning needs to be blueprinted.

Contrarians Synchronize beyond the Limit of Pairwise Interactions.

We give evidence that a population of pure contrarian globally coupled D-dimensional Kuramoto oscillators reaches a collective synchronous state when the interplay between the units goes beyond the limit of pairwise interactions. Namely, we will show that the presence of higher-order interactions may induce the appearance of a coherent state even when the oscillators are coupled negatively to the mean field. An exact solution for the description of the microscopic dynamics for forward and backward transitions is provided, which entails imperfect symmetry breaking of the population into a frequency-locked state featuring two clusters of different instantaneous phases.

Nonreciprocal Coupling Induced Self-Assembled Localized Structures.

Chains of coupled oscillators exhibit energy propagation by means of waves, pulses, and fronts. Nonreciprocal coupling radically modifies the wave dynamics of chains. Based on a prototype model of nonlinear chains with nonreciprocal coupling to nearest neighbors, we study nonlinear wave dynamics.