相关论文: Rotation numbers for quasiperiodically forced circ…
We study planar bicycle dynamics via the rotation number function associated with a closed front track and bicycle length R. We prove that mode-locking plateaus occur only at integer rotation numbers and that the rotation number function is…
We study locking of the modulation frequency of a relative periodic orbit in a general $S^1$-equivariant system of ordinary differential equations under an external forcing of modulated wave type. Our main result describes the shape of the…
We prove a sufficient condition for a \emph{pattern} $\pi$ on a \emph{triod} $T$ to have \emph{rotation number} $\rho_{\pi}$ coincide with an end-point of its \emph{forced rotation interval} $I_{\pi}$. Then, we demonstrate the existence of…
In this paper, we report the bifurcations of mode-locked periodic orbits occurring in maps of three or higher dimensions. The `torus' is represented by a closed loop in discrete time, which contains stable and unstable cycles of the same…
In a previous work by the authors the one dimensional (doubling) renormalization operator was extended to the case of quasi-periodically forced one dimensional maps. The theory was used to explain different self-similarity and universality…
In this paper two important aspects related to Caputo fractional-order discrete variant of a class of maps defined on the complex plane, are analytically and numerically revealed: attractors symmetry-broken induced by the fractional-order…
Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…
We analyze the dynamics of a charged particle moving in the presence of spatially-modulated magnetic fields. From Poincare surfaces of section and Liapunov exponents for characteristic trajectories we find that the fraction of pinned and…
We study parameter families of quasiperiodically forced (qpf) circle maps with Diophantine frequency. Under certain C1-open conditions concerning their geometry, we prove that these families exhibit nonuniformly hyperbolic behaviour, often…
We numerically study dynamical behaviors of the quasiperiodically forced Hodgkin-Huxley neuron and compare the dynamical responses with those for the case of periodic stimulus. In the periodically forced case, a transition from a periodic…
We extend rotation theory of circle maps to tiling spaces. Specifically, we consider a 1-dimensional tiling space $\Omega$ with finite local complexity and study self-maps $F$ that are homotopic to the identity and whose displacements are…
We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit…
We characterize the dynamical behavior of a clamped flexible fiber immersed in wall turbulence over a wide range of natural frequencies by means of direct numerical simulations. Only two flapping states are possible: one where the fiber…
The parameter dependence of the rotation number in families of circle maps which are perturbations of rational rotations is described. We show that if, at a critical parameter value, the map is a (rigid) rotation $x\to x+\frac{p}{q}~({\rm…
Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in…
We provide an explicit formula for an increment of the fibered rotation number of a one-parameter family of circle cocycles over any ergodic transformation in terms of invariant measures. As an application, for a family of random dynamical…
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We study invariant ergodic measures for quasiperiodically forced circle homeomorphisms and derive that either the system is uniquely ergodic or any such measure is associated to some invariant multigraph.
\emph{Rotation numbers} for some maps of \emph{triods} was introduced in \cite{BMR}. The goal of this paper is to study \emph{patterns} of \emph{triods} which don't force other \emph{patterns} with the same \emph{rotation number} which we…