Related papers: Logarithmically slow onset of synchronization
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…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
Weakly coupled oscillators adjust their dynamics to work in unison: they synchronize. This ubiquitous phenomenon is observed for oscillating pendulum, electronic devices, as well as clapping crowds or flashing fireflies. In effect,…
Two types of synchronization, Achronal Synchronization and Isochronous synchronization are investigated numerically when unidirectionally coupled laser systems are considered both on fast and slow dynamics by studying the correlation…
A coupled map lattice whose topology changes at each time step is studied. We show that the transversal dynamics of the synchronization manifold can be analyzed by the introduction of effective dynamical quantities. These quantities are…
Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical…
We investigate macroscopic behavior of a dynamical network consisting of a time-evolving wiring of interactions among a group of random walkers. We assume that each walker (agent) has an oscillator and show that depending upon the nature of…
The present study proposes a methodology that combines the 'Duffing oscillator system' and the 'Kuramoto oscillator network' to explore the synchronization of weak signals in dynamic systems. The first step of the procedure is to detect…
The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and…
I propose a discrete synchronization model of finite d-level systems and discuss what happens once superposition of states is allowed. The model exhibits various asymptotic behaviors that depend on the initial state. In particular, two…
A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature.…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…
We study synchronization of low-dimensional ($d=2,3,4$) chaotic piecewise linear maps. For Bernoulli maps we find Lyapunov exponents and locate the synchronization transition, that numerically is found to be discontinuous (despite…
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behaviour through a change of stability…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits…
We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation-invariant Hamiltonian. We show that dynamics starting from a random initial configuration…
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result…
Understanding the slowest relaxations of complex systems, such as relaxation of glass-forming materials, diffusion in nanoclusters, and folding of biomolecules, is important for physics, chemistry, and biology. For a kinetic system, the…