Related papers: Stably non-synchronizable maps of the plane
In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):…
The Kuramoto model is a classical nonlinear ODE system designed to study synchronization phenomena. Each equation represents the phase of an oscillator and the coupling between them is determined by a graph. There is an increasing interest…
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…
Inspired by work of Colding-Minicozzi on mean curvature flow, Zhang introduced a notion of entropy stability for harmonic map flow. We build further upon this work in several directions. First we prove the equivalence of entropy stability…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
The properties of functional relation between a non-invertible chaotic drive and a response map in the regime of generalized synchronization of chaos are studied. It is shown that despite a very fuzzy image of the relation between the…
We study the synchronization of two spatially extended dynamical systems where the models have imperfections. We show that the synchronization error across space can be visualized as a rough surface governed by the Kardar-Parisi-Zhang…
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…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
We show the existence of non-trivial self-expanding harmonic map flows starting from non-energy-minimizing 0-homogeneous maps to a regular ball or a closed hemisphere. In particular, given a non-minimizing but stationary 0-homogeneous…
We investigate the synchronization dynamics in a chain of coupled chaotic maps organized in a single-parent family tree, whose properties can be captured considering each parent node connected to two children, one of which also serves as…
Shared resources synchronization is a well studied problem, in both shared memory environment or distributed memory environment. Many synchronization mechanisms are proposed, with their own way to reach certain consistency level. This…
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
In the present Letter we show that the concept of the generalized synchronization regime in discrete maps needs refining in the same way as it has been done for the flow systems [PRE, 84 (2011) 037201]. We have shown that\alkor{, in the…
In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in…
Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…