Related papers: Stably non-synchronizable maps of the plane
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
A pair of graphs $(\Gamma,\Sigma)$ is called unstable if their direct product $\Gamma\times\Sigma$ admits automorphisms not from $\mathrm{Aut}(\Gamma)\times\mathrm{Aut}(\Sigma)$, and such automorphisms are said to be unexpected. The…
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…
We obtain stochastic stability of C2 non-uniformly expanding one-dimensional endomorphisms, requiring only that the first hyperbolic time map be L^{p}-integrable for p>3. We show that, under this condition (which depends only on the…
Although classical nonlinear dynamics suggests that sufficiently strong nonlinearity can sustain oscillations, quantization of such model typically yields a time-independent steady state that respects time-translation symmetry and thus…
A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient…
The stability analysis of synchronization in time-varying higher-order networked structures (simplicial complexes) is one of the challenging problem due to the presence of time-varying group interactions. In this context, most of the…
Synchronization is essential for proper functioning of the power grid. We investigate the synchronous state and its stability for a network with a cyclic topology and with the evolution of the states satisfying the swing equations. We…
In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average…
Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In this paper, we investigate the synchronization phenomena in a scale-free…
Some dynamical properties of nonlinear coupled systems can be described by the two-harmonic standard map, a two-dimensional area-preserving system with two parameters, where two distinct arbitrary resonant modes compete. Usually, the…
We show that the synchronized states of two systems of identical chaotic maps subject to either, a common drive that acts with a probability p in time or to the same drive acting on a fraction p of the maps, are similar. The synchronization…
We define auto- and cross-correlation functions capable to capture dynamical characteristics induced by local phase space structures in a general dynamical system. These correlation functions are calculated in the Standard Map for a range…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained…
This paper deals with the convergence analysis of the SUCPA (Semi Unsupervised Calibration through Prior Adaptation) algorithm, defined from a first-order non-linear difference equations, first developed to correct the scores output by a…
We study how a coupled array of spiking chaotic systems synchronizes to an external driving in a short time. Synchronization means spike separation at adjacent sites much shorter than the average inter-spike interval; a local lack of…
The complexity of modern control systems necessitates architectures that achieve high performance while ensuring robust stability, particularly for nonlinear systems. In this work, we tackle the challenge of designing output-feedback…
Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems…