English
Related papers

Related papers: Basins with tentacles

200 papers

Dissipative dynamical systems characterised by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space of such systems is structured around a…

Fluid Dynamics · Physics 2020-09-11 Miguel Beneitez , Yohann Duguet , Philipp Schlatter , Dan S. Henningson

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…

Numerical Analysis · Mathematics 2016-06-29 Roberto Cavoretto , Stefano De Marchi , Alessandra De Rossi , Emma Perracchione , Gabriele Santin

The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the…

Chaotic Dynamics · Physics 2015-10-28 André L. P. Livorati , Iberê L. Caldas , Carl P. Dettmann , Edson D. Leonel

In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in…

We consider a pendulum with vertically oscillating support and time-dependent damping coefficient which varies until reaching a finite final value. The sizes of the corresponding basins of attraction are found to depend strongly on the full…

Dynamical Systems · Mathematics 2015-06-29 James A. Wright , Michele Bartuccelli , Guido Gentile

Self-propelled colloids (swimmers) in confining geometries follow trajectories determined by hydrodynamic interactions with the bounding surfaces. However, typically these interactions are ignored or truncated to lowest order. We…

The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…

Chaotic Dynamics · Physics 2018-11-14 Yoshitaka Saiki , Miguel A. F. Sanjuan , James A. Yorke

In this paper we present a mechanism for the emergence of strange attractors in a one-parameter family of differential equations acting on a 3-dimensional sphere. When the parameter is zero, its flow exhibits an attracting heteroclinic…

Dynamical Systems · Mathematics 2021-11-05 Alexandre A. P. Rodrigues

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…

Dynamical Systems · Mathematics 2021-09-15 Joniald Shena , Konstantinos Kaloudis , Christos Merkatas , Miguel A. F. Sanjuán

The present paper investigates the binary system of quasars in the framework of the Circular Restricted Three-Body Problem. The parametric evolution of libration points, the geometry of zero-velocity curves are one of the crucial aspects of…

Chaotic Dynamics · Physics 2020-11-18 Vinay Kumar , Pankaj Sharma , Rajiv Aggarwal , Bhavneet Kaur

We analyze repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. This source of disorder leads to closed orbits with a variety of different periods, which can be orders of magnitude longer…

Adaptation and Self-Organizing Systems · Physics 2017-01-25 Darka Labavić , Hildegard Meyer-Ortmanns

We prove that the boundary of a component $U$ of the basin of an attracting periodic cycle (of period greater than 1) for an exponential map on the complex plane has Hausdorff dimension greater than 1 and less than 2. Moreover, the set of…

Dynamical Systems · Mathematics 2011-05-26 Krzysztof Barański , Bogusława Karpińska , Anna Zdunik

We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and…

Chaotic Dynamics · Physics 2012-03-20 Sabrina Camargo , Ricardo L. Viana , Celia Anteneodo

The ${\bf E}\times{\bf B}$ drift motion of particles in tokamaks provides valuable information on the turbulence-driven anomalous transport. One of the characteristic features of the drift motion dynamics is the presence of chaotic orbits…

We give a precise microlocal description of the singular profile that forms in the long-time propagation of internal waves in an effectively two-dimensional aquarium. We allow domains with corners, such as polygons appearing in the…

Analysis of PDEs · Mathematics 2025-06-18 Zhenhao Li

In this paper, we report an interesting kinematic phenomenon around the halos' edge related to the splashback radius. After the shell-crossing, cosmic flow exhibits various rotational morphologies via stream-mixing. Vorticity is generated…

Cosmology and Nongalactic Astrophysics · Physics 2022-12-07 Xiaolin Luo , Xiangling Xu , Xin Wang

We analyze the dynamical properties of a tetrahedron transformation on the space of non-degenerate tetrahedra which can be identified with the non-compact globally symmetric $8$-dimensional space $\mbox{Sl}(3,\mathbb{R}) /…

Differential Geometry · Mathematics 2017-08-29 Dimitris Vartziotis , Doris Bohnet

We explore thick accretion disks around rotating attractors. We detail the configurations analysing the fluid angular momentum and finally providing a characterization of the disk morphology and different possible topologies. Investigating…

High Energy Astrophysical Phenomena · Physics 2015-06-23 D. Pugliese , G. Montani

The basins of convergence, associated with the roots (attractors) of a complex equation, are revealed in the Hill problem with oblateness and radiation, using a large variety of numerical methods. Three cases are investigated, regarding the…

Chaotic Dynamics · Physics 2017-09-21 Euaggelos E. Zotos

The collective behavior of vibrated hexagonal disks confined in a monolayer is investigated experimentally. Due to the broken circular symmetry, hexagons prefer to rotate upon sufficiently strong driving. Due to the formation of liquid…

Soft Condensed Matter · Physics 2017-03-29 Manuel Baur , Kai Huang