Related papers: The saddle-straddle method to test for Wada basins

In dynamical systems, basins of attraction connect a given set of initial conditions in phase space to their asymptotic states. The basin entropy and related tools quantify the unpredictability in the final state of a system when there is…

Chaotic scattering in three dimensions has not received as much attention as in two dimensions so far. In this paper, we deal with a three-dimensional open Hamiltonian system whose Wada basin boundaries become non Wada when the critical…

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…

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins…

We study the noise-induced escape process in a prototype dissipative nonequilibrium system, the Ikeda map. In the presence of a chaotic saddle embedded in the basin of attraction of the metastable state, we find the novel phenomenon of a…

Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the…

We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes…

We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to…

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…

The rotating saddle not only is an interesting system that is able to trap a ball near its saddle point, but can also intuitively illustrate the operating principles of quadrupole ion traps in modern physics. Unlike the conventional models…

The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set or a $W$-set in a manifold. These are certain classes of compact invariant sets in whose vicinity the…

The Mackey-Glass system is a paradigmatic example of a delayed model whose dynamics is particularly complex due to, among other factors, its multistability involving the coexistence of many periodic and chaotic attractors. The prediction of…

Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global structure, metastability, and possible collective mechanisms of…

Escape from a potential well can occur in different physical systems, such as capsize of ships, resonance transitions in celestial mechanics, and dynamic snap-through of arches and shells, as well as molecular reconfigurations in chemical…

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…

We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect…

We use the saddle-approach, recently introduced in the numerical investigation of simple model liquids, in the analysis of a mean-field solvable system. The investigated system is the k-trigonometric model, a k-body interaction mean field…

Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling…

Results are presented from numerical simulations of the flat-space nonlinear Klein-Gordon equa- tion with an asymmetric double-well potential in spherical symmetry. Exit criteria are defined for the simulations that are used to help…

This report unravels frustration as a source of transient chaotic dynamics even in a simple array of coupled limit cycle oscillators. The transient chaotic dynamics along with the multistable nature of frustrated systems facilitates the…