Related papers: Phase description of chaotic oscillators
A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. The averaged motion equation of the system with infinitely…
We show that a lattice of phase oscillators with random natural frequencies, described by a generalization of the nearest-neighbor Kuramoto model with an additional cosine coupling term, undergoes a phase transition from a desynchronized to…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
We report the first experimental demonstration of chaotic phase synchronization (CPS) in unidirectionally coupled time-delay systems using electronic circuits. We have also implemented experimentally an efficient methodology for…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…
The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the…
This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for…
Synchronization phenomena, frequency shift and phase noise are often limiting key factors in the performances of oscillators. The perturbation projection method allows to characterize how the oscillator's output is modified by these…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…
Two identical chaotic oscillators that are mutually coupled via time delayed signals show very complex patterns of completely synchronized dynamics including stationary states and periodic as well as chaotic oscillations. We have…
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 explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which…
We study the pattern formation in a lattice of coupled phase oscillators with quenched disorder. In the synchronized regime concentric waves can arise, which are induced and increase in regularity by the disorder of the system. Maximal…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
Recently, a novel mixed-synchronization phenomenon is observed in counter-rotating nonlinear coupled oscillators. In mixed-synchronization state: some variables are synchronized in-phase, while others are out-of-phase. We have…
We report the observation of a novel and non-trivial synchronization state in a system consisting of three oscillators coupled in a linear chain. For certain ranges of coupling strength the weakly coupled oscillator pair exhibits phase…
To stabilize the periodic operation of a chemical reactor the oscillation period should be determined precisely in real time. The method discussed in the paper is based on adaptive sampling of the state variable with the use of chaotic…