相关论文: Direct transition to high-dimensional chaos throug…

We study and characterize a direct route to high-dimensional chaos (i.e. not implying an intermediate low-dimensional attractor) of a system composed out of three coupled Lorenz oscillators. A geometric analysis of this medium-dimensional…

For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". In high-dimensional chaotic attractors, trajectories are…

We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors…

Lorenz attractors are important objects in the modern theory of chaos. The reason from one side is that they are met in various natural applications (fluid dynamics, mechanics, laser dynamics, etc.). At the same time, Lorenz attractors are…

We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets…

The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…

This paper examines the most probable route to chaos in high-dimensional dynamical systems in a very general computational setting. The most probable route to chaos in high-dimensional, discrete-time maps is observed to be a sequence of…

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 itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…

Transition from quasiperiodicity with many frequencies (i.e., a high-dimensional torus) to chaos is studied by using $N$-dimensional globally coupled circle maps. First, the existence of $N$-dimensional tori with $N\geq 2$ is confirmed…

The method of generating of high-dimensional oscillations on the basis of summing of low-dimensional chaotic signals of noncoupled dynamical systems is investigated. It is shown that the correlation dimension of attractor reconstructed from…

We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…

We investigate the origin of various convective patterns using bifurcation diagrams that are constructed using direct numerical simulations. We perform two-dimensional pseudospectral simulations for a Prandtl number 6.8 fluid that is…

The classical Lorenz system is considered. For many years, this system has been the subject of study by numerous authors. However, until now the structure of the Lorenz attractor is not clear completely yet, and the most important question…

A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the…

In this work we study the existence of mechanisms of transition to global chaos in a closed Friedmann-Robertson-Walker universe with a massive conformally coupled scalar field. We propose a complexification of the radius of the universe so…

Unidirectionally coupled Lorenz systems in which the drive possesses a chaotic attractor and the response admits two stable equilibria in the absence of the driving is under investigation. It is found that double chaotic attractors coexist…

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…

Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…

We prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of C-infinity diffeomorphisms. This implies the existence of a C2- open domain in the space of dynamical systems with a…