Related papers: A unifying definition of synchronization for dynam…
We investigate the running sums of some well-known automatic sequences to determine whether they are synchronised.
Generalized synchronization of chaos is a type of cooperative behavior in directionally-coupled oscillators that is characterized by existence of stable and persistent functional dependence of response trajectories from the chaotic…
We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed…
Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
We show the first solvable chaotic synchronization model of unidirectionally coupled dynamical systems. We establish a new interpretation of the conditional Lyapunov exponent that characterizes chaotic synchronization completely. Moreover,…
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…
The phenomenon of spontaneous synchronization arises in a broad range of systems when the mutual interaction strength among components overcomes the effect of detuning. Recently it has been studied also in the quantum regime with a variety…
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or…
A new approach is proposed to the analysis of generalized synchronization of multidimensional chaotic systems. The approach is based on the symbolic analysis of discrete sequences in the basis of a finite T-alphabet. In fact, the symbols of…
We define the ``Pulse Synchronization'' problem that requires nodes to achieve tight synchronization of regular pulse events, in the settings of distributed computing systems. Pulse-coupled synchronization is a phenomenon displayed by a…
We present a theory for experimentally observed phenomenon of one dimensional asynchronous waves. The general principle of coexistence of linear and nonlinear solutions of a dynamical system is underlying the present theoretical work. The…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has…
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…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
We discuss in detail a human scale example of the synchronization phenomenon, namely the dynamics of the rhythmic applause. After a detailed experimental investigation, we describe the phenomenon with an approach based on the classical…
This paper deals with the chaotic oscillator synchronization. A new approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…