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We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates,…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
A new approach is proposed to the analysis of generalized synchronization of multidimensional chaotic systems. The approach is based on the symbolic analysis of discrete sequences in the basis of a finite T-alphabet. In fact, the symbols of…
Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system…
This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…
We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each…
We numerically investigate the dynamics of a closed chain of unidirectionally coupled oscillators in a regime of homoclinic chaos. The emerging synchronization regimes show analogies with the experimental behavior of a single chaotic laser…
In principle, the state space of a chaotic attractor can be partially or wholly reconstructed from interspike intervals recorded from experiment. Under certain conditions, the quality of a partial reconstruction, as measured by the spike…
We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged analogue of the Lorenz attractor. The attractors emerge near the…
Starting from Anosov chaotic dynamics of geodesic flow on a surface of negative curvature, we develop and consider a number of self-oscillatory systems including those with hinged mechanical coupling of three rotators and a system of…
Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial…
We present a phenomenological reduced-order model to capture the transition to thermoacoustic instability in turbulent combustors. The model is based on the framework of synchronization and considers the acoustic field and the unsteady heat…
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…
We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…
The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized…
This paper examines the use of operator-theoretic approaches to the analysis of chaotic systems through the lens of their unstable periodic orbits (UPOs). Our approach involves three data-driven steps for detecting, identifying, and…
We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and…