Related papers: Coupling-induced periodic windows in networked dis…

The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating - i.e. multiplicative -…

Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…

The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on…

Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli…

When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another…

We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of…

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…

The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…

Partially synchronized solitary states occur frequently when a synchronized system of networked oscillators is perturbed locally. Several asymptotic states of different frequencies can coexist at the same node. Here, we reveal the mechanism…

The dynamical equations of clarinet-like systems are known to be reducible to a non-linear iterated map within reasonable approximations. This leads to time oscillations that are represented by square signals, analogous to the Raman regime…

Identifying the hidden organizational principles and relevant structures of networks representing complex physical systems is fundamental to understand their properties. To this aim, uncovering the structures involving a network's prominent…

We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…

Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active…

Catastrophic failures are complete and sudden collapses in the activity of large networks such as economics, electrical power grids and computer networks, which typically require a manual recovery process. Here we experimentally show that…

We establish a criterion for the existence of a topological horseshoe in a class of planar systems generated by periodic switching between two subsystems, each admitting a family of closed orbits, where the mechanism for chaos arises from…

In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…

In this letter, we perform a sensitivity analysis on the master stability function approach for the synchronization of networks of coupled dynamical systems. More specifically, we analyze the linear stability of a nearly synchronized…

Coexisting periodic solutions of a dynamical system describing nonlinear optical processes of the second-order are studied. The analytical results concern both the simplified autonomous model and the extended nonautonomous model, including…