Related papers: Strange Nonchaotic Attractors
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the…
We study the random attractors associated with the stochastic fractional Schr\"odinger equation on $\mathbb{R}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schr\"odinger equation with Gaussian noise, we show…
This paper is concerned with the asymptotic behavior of solutions of the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. We first introduce a continuous…
This paper deals with various routes to hyperchaos with all three positive Lyapunov exponents in a three-dimensional quadratic map. The map under consideration displays strong hyperchaoticity in the sense that in a wider range of parameter…
Nonthermal attractors govern the emergent self-similar dynamics of far-from-equilibrium quantum systems, from ultrarelativistic nuclear collisions to cold-atom experiments. Within the framework of adiabatic hydrodynamization, the approach…
We investigate regular and chaotic dynamics of Two Bodies Swinging on a Rod, which differs from all the other mechanical analogies: depending on initial conditions, its oscillation could end very quickly and the reason is not a drag force…
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficients. We consider a special class of this type of systems…
We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e.…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large…
We study numerically chaotic behavior associated with a hyperbolic strange attractor of Plykin type in the model of Hunt, an artificially constructed dynamical system with continuous time. There are presented portraits of the attractor,…
In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate…
This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract…
A transition from a smooth torus to a chaotic attractor in quasiperiodically forced dissipative systems may occur after a finite number of torus-doubling bifurcations. In this paper we investigate the underlying bifurcational mechanism…
In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation.…
We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit…
In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a…
Attractors in asymmetric neural networks with deterministic parallel dynamics were shown to present a "chaotic" regime at symmetry eta < 0.5, where the average length of the cycles increases exponentially with system size, and an…
This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell. We will consider auto-oscillations arising on the level of enzyme-substrate interactions in the nutrient and respiratory…
We prove the existence and uniqueness of tempered random attractors for stochastic Reaction-Diffusion equations on unbounded domains with multiplicative noise and deterministic non-autonomous forcing. We establish the periodicity of the…