Related papers: Chaos as an Intermittently Forced Linear System
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
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…
Symbolic dynamics serves as a crucial tool in the study of chaotic systems, prompting extensive research into various methods for symbolic partitioning. The limitations of these methods are heuristic and empirical for the partition the…
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
The link between forced and free fluctuations for nonequilibrium systems can be described via a generalized version of the celebrated fluctuation-dissipation theorem. The use of the formalism of the Koopman operator makes it possible to…
The nonlinear dynamics of a recently derived generalized Lorenz model (Macek and Strumik, Phys. Rev. E 82, 027301, 2010) of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where…
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…
We consider a general N-degree-of-freedom nonlinear Hamiltonian system which is chaotic and dissipative and show that the origin of chaotic diffusion lies in the correlation of fluctuation of linear stability matrix for the equation of…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial state. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation…
We study, through a new perspective, a globally coupled map system that essentially interpolates between simple discrete-time nonlinear dynamics and certain long-range many-body Hamiltonian models. In particular, we exhibit relevant…
Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult…
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
This paper proposes an Extended-Kalman-Filter-like observer for parameter estimation during synchronization of chaotic systems. The exponential stability of the observer is guaranteed by a persistent excitation condition. This approach is…
In this chapter we present a new approach to the study of manifestations of chaos in real complex system. Recently we have achieved the following result. In real complex systems the informational measure of chaotic chatacter (IMC) can serve…