Related papers: A unifying definition of synchronization for dynam…
Synchronization of chaos arises between coupled dynamical systems and is very well understood as a temporal phenomena which leads the coupled systems to converge or develop a dependence with time. In this work, we provide a complementary…
The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems…
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently…
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 paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
A universal mechanism underlying generalized synchronization conditions in unidirectionally coupled stochastic oscillators is considered. The consideration is carried out in the framework of a modified system with additional dissipation.…
The phenomenon of spontaneous synchronization is universal and only recently advances have been made in the quantum domain. Being synchronization a kind of temporal correlation among systems, it is interesting to understand its connection…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
We introduce a novel concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset…
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an…
In this paper, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. An evolving hyper-network model is proposed for better describing some complex systems. A concept of joint degree is…
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
Recently, the synchronization of coupled dynamical systems has been widely studied. Synchronization is referred to as a process wherein two (or many) dynamical systems are adjusted to a common behavior as time goes to infinity, due to…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…