Related papers: Partial Synchronization and Partial Amplitude Deat…

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…

Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…

Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real world applications, the…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…

We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the…

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…

Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…

Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical…

Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and…

This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…

Synchronization of coupled continuous-time linear systems is studied in a general setting. For identical neutrally-stable linear systems that are detectable from their outputs, it is shown that a linear output feedback law exists under…

We have investigated the role that different connectivity regimes play on the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random connectivity…

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…

We study self-organized (s-) and driven (d-) synchronization in coupled map networks for some simple networks, namely two and three node networks and their natural generalization to globally coupled and complete bipartite networks. We use…

In this paper, we study the problem of synchronization with stochastic interaction among network components. The network components dynamics is nonlinear and modeled in Lure form with linear stochastic interaction among network components.…

We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability…

We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance in power-grids where energy is either…

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…

This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in…