Related papers: Multistability and nonsmooth bifurcations in the q…
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 study the phenomenon of mode-locking in the context of quasiperiodically forced non-linear circle maps. As a main result, we show that under certain C1-open condition on the geometry of twist parameter families of such systems, the…
The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions…
Synchronisation and stability under periodic oscillatory driving are well-understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly…
We show that introducing quenched disorder into a circle map leads to the suppression of quasiperiodic behavior in the limit of large system sizes. Specifically, for most parameters the fraction of disorder realizations showing…
The occurrence of strange non-chaotic attractors (SNA) in quasiperiodically forced systems has attracted considerable interest over the last two decades, in particular since it provides a rich class of examples for the possibility of…
We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar H\'{e}non map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two…
We investigate the dynamics of an injection locked in-plane uniform spin torque oscillator for several forcing configurations at large driving amplitudes. For the analysis, the spin wave amplitude equation is used to reduce the dynamics to…
There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…
Intermittent strange nonchaotic attractors (SNAs) appear typically in quasiperiodically forced period-doubling systems. As a representative model, we consider the quasiperiodically forced logistic map and investigate the mechanism for the…
We introduce and study a physically motivated problem that exhibits interesting and perhaps unexpected mathematical features. A cellular flow is a two-dimensional Hamiltonian flow of the Hamiltonian $H(x, y) = \cos(x) \cos(y)$. We study a…
Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a…
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.…
The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose…
A transition from a smooth torus to a chaotic attractor in quasiperiodically forced dissipative systems may occur after a finite number of torus-doubling bifurcations. In this paper we investigate the underlying bifurcational mechanism…
We describe the relation between the dynamical properties of a quasiperiodically forced orientation-preserving circle homeomorphism and the behavior of the fibered rotation number with respect to strictly monotone perturbations. Despite the…
We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…
Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a…
We study nonsmooth bifurcations of four types of families of one-dimensional quasiperiodically forced maps of the form $F_i(x,\theta) = (f_i(x,\theta), \theta+\omega)$ for $i=1,\dots,4$, where $x$ is real, $\theta\in\mathbb{T}$ is an angle,…
We present an experimental and theoretical study of the effect of spatio-temporal fluctuations in quasi-reversible systems displaying a spatial quintic supercritical bifurcation. The saturation mechanism is drastically changed by the…