Related papers: How to detect Wada Basins
Noisy scattering dynamics in the randomly driven H\'enon-Heiles system is investigated in the range of initial energies where the motion is unbounded. In this paper we study, with the help of the exit basins and the escape time…
We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some…
The lakes of Wada are three disjoint simply connected domains in $S^2$ with the counterintuitive property that they all have the same boundary. The common boundary is a indecomposable continuum. In this article we calculated the Minkowski…
In this paper, a two parameters family $F_{\beta_1,\beta_2}$ of maps of the plane living two different subspaces invariant is studied. We observe that, our model exhibits two chaotic attractors $A_i$, $i=0,1$, lying in these invariant…
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…
Transport properties of a single-mode waveguide with rough boundary are studied by discrimination between two mechanisms of surface scattering, the amplitude and square-gradient ones. Although these mechanisms are generically mixed, we show…
We study the dynamics of the geodesics of pp-wave spacetimes with polynomial profiles, which are dynamically equivalent to the motion of a classical particle in a two-dimensional harmonic polynomial potential. We demonstrate that the Wada…
We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final…
To explore basin geometry in high-dimensional dynamical systems, we consider a ring of identical Kuramoto oscillators. Many attractors coexist in this system; each is a twisted periodic orbit characterized by a winding number $q$, with…
The escape dynamics in a two-dimensional multiwell potential is explored. A thorough numerical investigation is conducted in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional…
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orbits of a given dynamical system. We develop theory for it…
Real-world systems often evolve on different timescales and possess multiple coexisting stable states. Whether or not a system returns to a given stable state after being perturbed away from it depends on the shape and extent of its basin…
Research in multistable systems is a flourishing field with countless examples and applications across scientific disciplines. I present a catalog of multistable dynamical systems covering relevant fields of knowledge. This work is focused…
The detection of coherent structures is an important problem in fluid dynamics, particularly in geophysical applications. For instance, knowledge of how regions of fluid are isolated from each other allows prediction of the ultimate fate of…
We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.
The basin of attraction is the set of initial points that will eventually converge to some attracting set. Its knowledge is important in understanding the dynamical behavior of a given dynamical system of interest. In this work, we address…
In this article, we present a bifurcation analysis on the double-diffusive convection. Two pattern selections, rectangles and squares, are investigated. It is proved that there are two different types of attractor bifurcations depending on…
This paper investigates the symmetry properties of basins of attraction and their boundaries in equivariant dynamical systems. While the symmetry groups of compact attractors are well understood, the corresponding analysis for non-compact…
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation…
Previous works have been devoted to the study of two-dimensional noninvertible maps, obtained using a coupling between one-dimensional logistic maps. This paper is devoted to the study of a specific one, in order to complete previous…