Related papers: Stably non-synchronizable maps of the plane
Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the…
In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive…
Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…
We introduce two generalizations of synchronizability to automata with transitions weighted in an arbitrary semiring K=(K,+,*,0,1). (or equivalently, to finite sets of matrices in K^nxn.) Let us call a matrix A location-synchronizing if…
We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues…
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…
We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…
We construct and analyze solutions to a regularized homogeneous $p$-harmonic map flow equation for general $p \geq 2$. The homogeneous version of the problem is new and features a monotonicity formula extending the one found by Struwe for…
The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In the autonomous version, such a system is a set of functions x:R{\to}{0,1}^{n} called states (R is the time…
We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each…
A new type of nonlinear time series analysis is introduced, based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit…
The phenomenology of a system of two coupled quadratic maps is studied both analytically and numerically. Conditions for synchronization are given and the bifurcations of periodic orbits from this regime are identified. In addition, we show…
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…
Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
We study the synchronization of two chaotic maps with unidirectional (master-slave) coupling. Both maps have an intrinsic delay $n_1$, and coupling acts with a delay $n_2$. Depending on the sign of the difference $n_1-n_2$, the slave map…
Coupled cell systems model interacting dynamical units and provide a natural framework for studying synchrony phenomena arising from collective behavior. Graph symmetries often induce such patterns, but certain networks exhibit additional…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic…