Related papers: Basins with tentacles
The well known butterfly effect got its nomenclature from its two wings geometrical structure in phase space. There are chaotic dynamics from simple one-wing to multiple-wings complex structures in phase space. In this communication we…
A key challenge of nonlinear dynamics and network science is to understand how higher-order interactions influence collective dynamics. Although many studies have approached this question through linear stability analysis, less is known…
In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect…
We solve for the dynamics of a pair of spins, coupled to each other and also to an environmental sea of oscillators. The environment mediates an indirect interaction between the spins, causing both mutual coherence effects and dissipation.…
The generation of entanglement between two oscillators that interact via a common reservoir is theoretically studied. The reservoir is modeled by a one-dimensional harmonic crystal initially in thermal equilibrium. Starting from a separable…
Phase space trajectories are fundamentally important for understanding and analysing chaotic attractors. This is mostly carried out by direct numerical solution of the dynamical equations. Though the origin of scrolls can be understood from…
In this paper, we show that equiangular spirals (also known as logarithmic spirals) appear naturally in fluids going through sinks. We provide a simple mathematical model that explains the spiral forms in some natural formations. For this…
Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys.…
We construct a diffeomorphism of $\mathbb{T}^3$ admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting $T\mathbb{T}^3 = E^{cs} \oplus E^u$ and can be made…
The inertia of particles driven by the turbulent flow of the surrounding fluid makes them prefer certain regions of the flow. The heavy particles lag behind the flow and tend to accumulate in the regions with less vorticity, while the light…
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…
Dissipating of disorder quantum vortices in an annular two-dimensional Bose-Einstein condensate can form a macroscopic persistent flow of atoms. We propose a protocol to create persistent flow with high winding number based on a double…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
In this paper the geodesics of an open multiply connected hyperbolic manifold are presented from the dynamical system point of view. The approach is completely numerical. Similar to the closed hyperbolic case there is a zero-measure set of…
Warps are common features in both stellar and gaseous disks of nearby spiral galaxies with the latter usually easier to detect. Several theories have been proposed in the literature to explain their formation and prevalence, including tidal…
An {\em attractor} is a transitive set of a flow to which all positive orbit close to it converges. An attractor is {\em singular-hyperbolic} if it has singularities (all hyperbolic) and is partially hyperbolic with volume expanding central…
A basic problem in dynamics is to identify systems with positive entropy, i.e., systems which are "chaotic." While there is a vast collection of results addressing this issue in topological dynamics, the phenomenon of positive entropy…
For each prime number $p$, the dynamical behavior of the square mapping on the ring $\mathbb{Z}_p$ of $p$-adic integers is studied. For $p=2$, there are only attracting fixed points with their attracting basins. For $p\geq 3$, there are a…
We study a one-dimensional lattice gas "dynamical geometry model" in which local reversible interactions of counter-rotating groups of particles on a ring can create or destroy lattice sites. We exhibit many periodic orbits and and show…
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which…