相关论文: On numerical study of attractors of ODEs

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.…

A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…

A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approach is offered that effectively propagates the statistics in time. Loss of sensitivity to an…

Dominance of Milnor attractors in high-dimensional dynamical systems is reviewed, with the use of globally coupled maps. From numerical simulations, the threshold number of degrees of freedom for such prevalence of Milnor attractors is…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…

The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical…

An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system $\mathcal{E}$ with respect to weak and strong topologies was introduced in [8] primarily to study the long-time behavior of the 3D Navier-Stokes…

Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…

In the dynamical systems approach to describing turbulent or otherwise chaotic flows, an important quantity is the Lyapunov exponents and vectors that characterize the strange attractor of the flow. In particular, knowledge of the Lyapunov…

Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase.…

Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…

This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…

This work analyzes trajectories obtained by YOLO and DeepSORT algorithms of dense emulsion systems simulated by Lattice Boltzmann methods. The results indicate that the individual droplet's moving direction is influenced more by the…

The use of iteration and piecewise functions allows analytic expression of the trajectories of an R\"ossler-like attractor, avoiding infinite series solution. It seems possible to extend this approach to other attractors, even if the…

Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…

In this paper, we consider three-dimensional dynamical systems, as for example the Lorenz model. For these systems, we introduce a method for obtaining families of two-dimensional surfaces such that trajectories cross each surface of the…

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…

This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as…

We use simple equations in order to compare the basins of attraction on the complex plane, corresponding to a large collection of numerical methods, of several order. Two cases are considered, regarding the total number of the roots, which…

In this work we present a set-oriented path following method for the computation of relative global attractors of parameter-dependent dynamical systems. We start with an initial approximation of the relative global attractor for a fixed…