Related papers: Abstract basins of attraction
We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this…
Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
The origin and meaning of facial beauty represent a longstanding puzzle. Despite the profuse literature devoted to facial attractiveness, its very nature, its determinants and the nature of inter-person differences remain controversial…
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…
The circular Sitnikov problem, where the two primary bodies are prolate or oblate spheroids, is numerically investigated. In particular, the basins of convergence on the complex plane are revealed by using a large collection of numerical…
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 present work deals with the recently introduced restricted six body-problem with square configuration. It is determined that the total number of libration points are twelve and twenty for the mass parameter $0< \mu < 0.25$. The…
Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize the riddled basin using the uncertainty…
A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely…
Artists spent a great deal of time studying anatomy for precise rendering of the human body as well as light, shadows, and perspective for convincing representation of the three-dimensional world. But in many paintings, they also had to…
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new way. Our…
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…
In many applications one is interested in finding the stability regions (basins of attraction) of some stationary states (attractors). In this paper we show that one cannot compute, in general, the basins of attraction of even very regular…
Marginally outer trapped surfaces (also referred to as apparent horizons) that are stable in 3-dimensional initial data sets obeying the dominant energy condition strictly are known to satisfy an area bound. The main purpose of this note is…
It is common that the average length of chaotic transients appearing as a consequence of crises in dynamical systems obeys a power low of scaling with the distance from the crisis point. It is, however, only a rough trend; in some cases…
A study of rational maps of the real or complex projective plane of degree two or more, concentrating on those which map an elliptic curve onto itself, necessarily by an expanding map. We describe relatively simple examples with a rich…
The planar circular restricted three-body problem with modified Newtonian gravity is used in order to determine the Newton-Raphson basins of attraction associated with the equilibrium points. The evolution of the position of the five…
It is shown that the incorporation of linear sink/source terms in the three-wave resonance interaction model results in the time dependence of the wave amplitudes, which could exhibit the properties of a strange attractor. This finding…
In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction…