Related papers: The saddle-straddle method to test for Wada basins
We consider the motion of a droplet bouncing on a vibrating bath of the same fluid in the presence of a central potential. We formulate a rotation symmetry-reduced description of this system, which allows for the straightforward application…
We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet that is periodically kicked with a delta function…
The cavity method is one of the cornerstones of the statistical physics of disordered systems such as spin glasses and other complex systems. It is able to analytically and asymptotically exactly describe the equilibrium properties of a…
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the…
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
Finding saddle points of dynamical systems is an important problem in practical applications such as the study of rare events of molecular systems. Gentlest ascent dynamics (GAD) is one of a number of algorithms in existence that attempt to…
Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a…
We reveal the escape mechanism of orbits in a Hamiltonian system with four exit channels composed of two-dimensional perturbed harmonic oscillators. We distinguish between trapped chaotic, non-escaping regular and escaping orbits by…
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 consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…
Saddle-point configurations, such as the Euclidean bounce and sphalerons, are known to be difficult to find numerically. In this Letter we study a new method, Quartic Gradient Flow, to search for such configurations. The central idea is to…
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…
We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid, and apply it to the Bader charge partitioning for the electron charge density. Starting with the…
The wake of a body moving across the isopycnals of a strongly stratified fluid is characterized by the presence of an intense jet which, under certain circumstances, may become unstable. To get insight into the phenomenology of this…
The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g. boundary layer flows. The dynamical…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…
The tribology of a sliding elastic continuum in contact with a disordered substrate is investigated analytically and numerically via a bead-spring model. The deterministic dynamics of this system exhibits a depinning transition at a finite…
Population dynamics in systems composed of cyclically competing species has been of increasing interest recently. Here, we investigate a system with four or more species. Using mean field theory, we study in detail the trajectories in…
The Lotka-Volterra model of competition has been studied by numerical simulations using the Runge-Kutta-Fehlberg algorithm. The stable fixed points, unstable fixed point, saddle node, basins of attraction, and the separatices are found. The…