Related papers: Hidden symmetry and Collective behavior
We quantify nonlinear interactions between coupled complex processes, when the system is subject to noise and not all its components are measurable. Our method is applicable even when the system cannot be continuously monitored over time,…
We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the…
Synchronization among globally coupled, chaotic map lattices can be related to stable periodic windows in isolated chaotic maps. This relation provides a simple predictive tool for the understanding of complicated behavior in coupled…
We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…
We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic…
We study a synchronization mechanism, based on one-way coupling of all-or-nothing type, applied to coupled map lattices with several different local rules. By analyzing the metric and the topological distance between the two systems, we…
We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention…
Some aspects of the geometry and the dynamics of generalized Chaplygin systems are investigated. First, two different but complementary approaches to the construction of the reduced dynamics are reviewed: a symplectic approach and an…
In this paper we present a generalized analytical solution to the generalized state equations of coupled second-order non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of…
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…
The coexistence of coherently and incoherently oscillating parts in a system of identical oscillators with symmetrical coupling, i.e., a chimera state, is even observable with uniform global coupling. We address the question of the…
Owing to the absence of the phase space attractors in the Hamiltonian dynamical systems, the concept of the identical synchronization between the dissipative systems is inapplicable to the Hamiltonian systems for which, thus, one defines a…
Spontaneous synchronisation is a collective phenomenon that can occur in both dynamical classical and quantum systems. Here, we analyse the spontaneous synchronisation dynamics of vibrations assisting energy transfer in a bio-inspired…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…
We investigate quantum synchronization phenomenon within the complex network constituted by coupled optomechanical systems and prove the unknown identical quantum states can be shared or distributed in the quantum network even though the…