Related papers: Controlling unstable chaos: Stabilizing chimera st…
Chimera states consisting of domains of coherently and incoherently oscillating nonlocally-coupled phase oscillators in systems with spatial inhomogeneity are studied. The inhomogeneity is introduced through the dependence of the oscillator…
In a recent study of chaos synchronization in symmetric complex networks [Pecora \textit{et al}., Nat. Commun. {\bf 5}, 4079 (2014)], it is found that stable synchronous clusters may coexist with many non-synchronous nodes in the…
We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the…
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach…
We report on a significant improvement of the classical time-delayed feedback control method for stabilization of unstable periodic orbits or steady states. In an electronic circuit experiment we were able to realize time-varying and…
We propose a control scheme which can stabilize and fix the position of chimera states in small networks. Chimeras consist of coexisting domains of spatially coherent and incoherent dynamics in systems of nonlocally coupled identical…
We present a methodology for synchronization of chaotic oscillators with linear feedback control. The proposed method is based on analyzing the chaotic oscillator as a multi-mode linear system and deriving sufficient conditions for…
In this work, we demonstrate the open-loop control of chaotic systems by means of optimized periodic signals. The use of such signals enables us to reduce control power significantly in comparison to simple harmonic perturbations. It is…
Symmetry broken states arise naturally in oscillatory networks. In this Letter, we investigate chaotic attractors in an ensemble of four mean-coupled Stuart-Landau oscillators with two oscillators being synchronized. We report that these…
Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit,…
Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed…
We consider the decoherence of a pseudo-spin ensemble under collective random rotations, and study, both theoretically and experimentally, how a nondestructive measurement combined with real-time feedback correction can protect the state…
Chimera is a rich and fascinating class of self-organized solutions developed in high dimensional networks having non-local and symmetry breaking coupling features. Its accurate understanding is expected to bring important insight in many…
Arrays of identical limit-cycle oscillators have been used to model a wide variety of pattern-forming systems, such as neural networks, convecting fluids, laser arrays, and coupled biochemical oscillators. These systems are known to exhibit…
Systems of coupled oscillators have been seen to exhibit chimera states, i.e. states where the system splits into two groups where one group is phase locked and the other is phase randomized. In this work, we report the existence of chimera…
Chimera states have attracted significant attention as symmetry-broken states exhibiting the unexpected coexistence of coherence and incoherence. Despite the valuable insights gained from analyzing specific systems, an understanding of the…
Synchronization of weakly-coupled non-linear oscillators is a ubiquitous phenomenon that has been observed across the natural sciences. We study the dynamics of optomechanical arrays - networks of mechanically compliant structures that…
Chimera states in coupled oscillator systems present both spatially coherent and incoherent domains. The number and size of these domains depend on many factors like the system parameters and initial conditions. Systematic investigations of…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
This paper presents a framework to perform bifurcation analysis in laboratory experiments or simulations. We employ control-based continuation to study the dynamics of a macroscopic variable of a microscopically defined model, exploring the…