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Synchronization is a fundamental phenomenon in dynamical systems, occurring in a wide range of contexts such as mechanical, chemical, biological, and social systems. In this work, we explore a novel manifestation of synchronization in…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit…
The property of desynchronization in an all-to-all network of homogeneous impulse-coupled oscillators is studied. Each impulse-coupled oscillator is modeled as a hybrid system with a single timer state that self-resets to zero when it…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multi-layered structure of connections affects the synchronization properties of dynamical systems evolving…
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…
It is widely held that identical systems tend to behave similarly under comparable conditions. Yet, for systems that interact through a network, symmetry breaking can lead to scenarios in which this expectation does not hold. Prominent…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number…
Cluster synchronization is a phenomenon in which oscillators in a given network are partitioned into synchronous clusters. As recently shown, diverse cluster synchronization patterns can be found using network symmetry when the oscillators…
Bump attractors are wandering localised patterns observed in in vivo experiments of spatially-extended neurobiological networks. They are important for the brain's navigational system and specific memory tasks. A bump attractor is…
Synchronisation and pattern formation have been intensely addressed for systems evolving on static networks. Extending the study to include the inherent ability of the network to adjust over time proved cumbersome and led to conclusions…
We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional…