Oscillatory activity in the central nervous system is associated with various functions, like motor control, memory formation, binding, and attention. Quasiperiodic oscillations are rarely discussed in the neurophysiological literature yet they may play a role in the nervous system both during normal function and disease. Here we use a physical system and a model to explore scenarios for how qu...

We consider a class of ordinary differential equations describing one-dimensional analytic systems with a quasiperiodic forcing term and in the presence of damping. In the limit of large damping, under some generic nondegeneracy condition on the force, there are quasiperiodic solutions which have the same frequency vector as the forcing term. We prove that such solutions are Borel summable at t...

We derive a criterion for the positivity of maximal Lyapunov exponent generic mixed random-quasiperiodic linear cocycles, model introduced in previous work. This result is applicable to cocycles corresponding Schr\"odinger operators with randomly perturbed quasiperiodic potentials. Moreover, we establish an average uniform convergence Oseledets theorem.

Reciprocal space engineering allows tailoring the scattering response of media with a low refractive-index contrast. Here it is shown that quasiperiodic leveled-wave structure well-defined reciprocal and random real distribution can be engineered to open complete photonic bandgap (CPBG) for any For these structures, an analytical estimation derived, which predicts there optimal number Bragg pea...

A review of the experimental evidence which rejects the determination of the Icosahedral phase as periodic is presented. The experiments discussed include various diffraction techniques for the study of the long range order as well the methods to determine the local atomic arrangement.

We study analytically the (N-1)-fold degenerate Hopf bifurcation at which N stationary modes with identical parameters become unstable in a model of a solid-state laser with intracavity second harmonic generation. We use the normal form method and exploit the symmetries of the problem. Up to N=3, stable periodic antiphased solutions emerge from the Hopf bifurcation. For N=4, stable quasiperiodi...