Related papers: Structure analysis of the Lorenz-84 chaotic attrac…
The predictability of weather and climate is strongly state-dependent: special and extremely relevant atmospheric states like blockings are associated with anomalous instability. Indeed, typically, the instability of a chaotic dynamical…
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…
A three-component dynamic system with influence of pumping and nonlinear dissipation describing a quantum cavity electrodynamic device is studied. Different dynamical regimes are investigated in terms of divergent trajectories approaches…
We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of…
In this paper a Lorenz-like system, describing the process of rotating fluid convection, is considered. The present work demonstrates numerically that this system, also like the classical Lorenz system, possesses a homoclinic trajectory and…
Dynamical and statistical properties of tracer advection are studied in a family of flows produced by three point-vortices of different signs. A collapse of all three vortices to a single point is then possible. Tracer dynamics is analyzed…
A new method of symbolic analysis based on finite discretization of velocity-curvature space is proposed. A minimum alphabet is introduced in a natural way, and a number of initial analytic measures are defined that make it possible to…
We consider both the dynamics within and towards the supercycle attractors along the period-doubling route to chaos to analyze the development of a statistical-mechanical structure. In this structure the partition function consists of the…
An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original and reconstructed attractors may not be topologically…
In this paper the dynamics of a fractional order system modelling the interaction between dark matter and dark energy is analytically and numerically studied. It is shown for the first time that systems modelling the interaction between…
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…
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…
This article confronts the formidable task of exploring chaos within hidden attractors in nonlinear 3-D autonomous systems, highlighting the lack of established analytical and numerical methodologies for such investigations. As the basin of…
Poincar\'e recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to…
We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback…
A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional…
Lorenz attractors play an important role in the modern theory of dynamical systems. The reason is that they are robust, i.e. preserve their chaotic properties under various kinds of perturbations. This means that such attractors can exist…
Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated…
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,…
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.