Related papers: Dirac synchronization is rhythmic and explosive
In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on…
A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical…
Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…
The transition to global synchronization in coupled dynamical systems is governed by the interplay between coupling strength and structural topology. Although abrupt, first-order-like synchronization transitions have been extensively…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…
In many real-world systems, partial synchronization is the dominant dynamical regime and, in systems such as the brain, is often accompanied by collective oscillations in which multiple overlapping modes interact to produce complex rhythmic…
A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a…
In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
Adaptive dynamical networks are network systems in which the structure co-evolves and interacts with the dynamical state of the nodes. We study an adaptive dynamical network in which the structure changes on a slower time scale relative to…
Neuronal network synchronization has received wide interests. Network connection structure is known to play a key role in its synchronization. In the present manuscript, we study the influence of initial membrane potentials together with…
Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling.…
Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not…
We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is…
Temporal networks are an important type of network whose topological structure changes over time. Compared with methods on static networks, temporal network embedding (TNE) methods are facing three challenges: 1) it cannot describe the…
In this paper the collective dynamics of $N$-coupled piecewise linear (PWL) systems with different number of scrolls and coupled in a master-slave sequence configuration is studied, i.e. a ring connection with unidirectional links.…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…
We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In…