Related papers: Rotation numbers for quasiperiodically forced circ…
We investigate numerically complex dynamical systems where a fixed point is surrounded by a disk or ball of quasiperiodic orbits, where there is a change of variables (or conjugacy) that converts the system into a linear map. We compute…
We argue that certain materials exhibit asymmetry of their mechanical and conducting properties with respect to clockwise/counterclockwise rotation. We show that a cylinder made of a suitably chosen semiconductor coated in a metallic film…
We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on…
Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…
In this paper we are concerned with quasi-periodic forced one dimensional maps. We consider a two parametric family of quasi-periodically forced maps such that the one dimensional map (before forcing) is unimodal and it has a full cascade…
We experimentaly investigate higher-order seeded modulation instability in an optical fiber experiment. The recirculating loop configuration with round-trip losses compensation enables the observation in single-shot of the spatio-temporal…
We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in…
Quasiperiodicity, a partially synchronous state that precedes the onset of forced synchronization in hydrodynamic systems, exhibits distinct geometrical patterns based on the specific route to lock-in. In this study, we explore these…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…
A less studied numerical characteristic of periodic orbits of area preserving twist maps of the annulus is the twist or torsion number, called initially the amount of rotation. It measures the average rotation of tangent vectors under the…
Weakly damped mechanical systems under small periodic forcing tend to exhibit periodic response in a close vicinity of certain periodic orbits of their conservative limit. Specifically, amplitude frequency plots for the conservative limit…
Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems such as two-frequency forced Faraday waves, we study the interaction of two spatially periodic modes that are nearly resonant. Within the…
The dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the…
Recently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the…
This article presents an adaptive Super-Twisting Sliding Mode Control framework for uncertain first-order systems, with rate-bounded perturbations, where the bound is constant but unknown. Positive definite barrier functions, when used in…
We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
In this paper, we focus on a numerical technique, the weighted Birkhoff average (WBA) to distinguish between four categories of dynamics for quasiperiodically-forced circle maps. Regular dynamics can be classified by rotation vectors, and…
Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…