Related papers: How to detect Wada Basins

We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the…

We study some topological properties of attractors.

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to…

In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal…

We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…

An attractor of a dynamical system may represent the system's 'desirable' state. Perturbations to the system may push the system out of the basin of attraction of the desirable attractor and into undesirable states. Hence, it is important…

Fractal surfaces are ubiquitous in nature as well as in the sciences. The examples range from the cloud boundaries to the corroded surfaces. Fractal dimension gives a measure of the irregularity in the object under study. We present a…

In applied sciences, such as physics and biology, it is often required to model the evolution of populations via dynamical systems. In this paper, we focus on the problem of approximating the basins of attraction of such models in case of…

This letter presents a new approach using the cosmic peculiar velocity field to characterize the morphology and size of large scale structures in the local Universe. The algorithm developed uses the three-dimensional peculiar velocity field…

This article explores in depth a watershed concept to partition the universe, introduced in \cite{2019MNRAS.489L...1D} and applied to the {\it Cosmicflows-3} observational dataset. We present a series of tests conducted with cosmological…

There exist Lakes of Wada in $\mathbb S^n, n\ge 3,$ which are quasiconformally equivalent to a Euclidean ball and are John domains.

From the striped coats of zebras to the ripples in windblown sand, the natural world abounds with locally banded patterns. Such patterns have been of great interest throughout history, and, in the last twenty years, scientists in a wide…

We want to consider Martin boundary theory applied to inhomogeneous fractals. This is under some conditions possible, but up to now it is not clear, how one can easily check, if a certain fractal fulfills those conditions. We want to…

We consider the problem of classifying the dynamics of complex polynomials $f: \mathbb{C} \to \mathbb{C}$ restricted to their basins of infinity. We synthesize existing combinatorial tools --- tableaux, trees, and laminations --- into a new…

We suggest the numerical approach to detect eigenfrequencies of trapped modes in waveguides or guided waves in diffraction gratings. At the same time, the approach works perfectly for computation of systems with finitely many scattering…

We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their…

Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and…

In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models. Precisely, a particular solution of a…

The microscopic description of the local structure of water remains an open challenge. Here, we adopt an agnostic approach to understanding water's hydrogen bond network using data harvested from molecular dynamics simulations of an…

Different approaches are presented to investigate diffusion from a point source in a slab delimited by two absorbing boundaries consisting of parallel infinite planes. These approaches enable to consider the effect of absorption at the…