Related papers: Bubbling in Oscillator Networks
Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise.…
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…
We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here we leverage this relation to study a class of networks for which the threshold…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system…
Spatiotemporal chaos in the form of defect-mediated turbulence is known for oscillators coupled by diffusion. Here we explore the same conditions that produce defect turbulence, in an array of oscillators that are coupled through the…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
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…
Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with…
We study synchronization processes in networks of slightly non identical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in…
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic…
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…
Heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators. Scale-free networks display a great deal of heterogeneity, containing a few nodes, termed hubs,…
In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…
We investigate the role of connection density in an adaptive network model of chaotic units that dynamically rewire based on their internal states and local coherence. By systematically varying the network's connectivity density, we uncover…
We investigate synchronization in complex networks of noisy phase oscillators. We find that, while too weak a coupling is not sufficient for the whole system to synchronize, too strong a coupling induces a nontrivial type of phase slip…
Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a…