We study the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behavior. We study these transitions in detail for small and large numbers of oscillators. P...

We discuss the time-discrete parametrized synchronous dynamics of two coupled chaotic neuromodules. The symmetrical coupling of identical 2-neuron modules results in periodic, quasiperiodic as well as chaotic dynamics constrained to a synchronization manifold M . Stability of the synchonized dynamics is calculated by transversal Lyapunov exponents. In addition to synchronized attractors there o...

A cluster for the octagonal square-rhombus tiling is presented, which has the property that among all tilings completely covered by the cluster the perfectly quasiperiodic and eightfold symmetric ones have the highest cluster density. Since on these eightfold symmetric tilings there is considerable overlap of clusters, it seems likely that these tiling have the highest cluster density even amon...

A simple numerical method to study the effect of an applied magnetic field on the energy spectrum of non-periodic superlattice structures is presented. The magnetic field could be either parallel or perpendicular to the growth direction. Our method is based on the transfer matrix technique and on the effective mass approximation. We discuss the advantages and disadvantages of the proposed appro...

Three-dimensional instability modes of the periodic flow in a rectangular cavity driven by the harmonic sliding oscillation of its floor are explored experimentally. Theory for a cavity with infinite span predicts two synchronous modes and a quasiperiodic traveling-wave mode as primary transitions from two-dimensional to three-dimensional flow for different combinations of floor oscillation amp...

We study electronic properties as a function of the six types of local environments found in the octagonal tiling. The density of states has six characteristic forms, although the detailed structure differs from site to site since no two sites are equivalent in a quasiperiodic tiling. We present the site-dependent magnetic susceptibility of electrons on this tiling, which also has six character...

We investigate zero-field Ising models on periodic approximants of planar quasiperiodic tilings by means of partition function zeros and high-temperature expansions. These are obtained by employing a determinant expression for the partition function. The partition function zeros in the complex temperature plane yield precise estimates of the critical temperature of the quasiperiodic model. Conc...

It has been known that noise can suppress multistability by dynamically connecting coexisting attractors in the system which are otherwise in separate basins of attraction. The purpose of this minireview is to argue that quasiperiodic driving can play a similar role in suppressing multistability. A concrete physical example is provided where quasiperiodic driving was demonstrated to eliminate m...