In this paper I will investigate the bifurcation and asymptotic behavior of solutions of the Swift-Hohenberg equation and the generalized Swift-Hohenberg equation with the Dirichlet boundary condition on a onedimensional domain (0, L). I will also study the bifurcation and stability of patterns in the n-dimensional Swift-Hohenberg equation with the odd-periodic and periodic boundary conditions....

Admittance diagrams are used to analyze qualitatively and quantitatively the behavior of inhomogeneous thin films with an arbitrary refractive-index function. From this study it follows that one can treat the behavior of rugate filters by using the concept of effective refractive indices, which are associated with the phase integral in a simple way. These results are applied to the study of per...

We investigate the effects of quenched disorder on the coherent response in a driven system of coupled oscillators. In particular, the interplay between quenched noise and periodic driving is explored, with particular attention to the possibility of resonance. The phase velocity is examined as the response of the system; revealed is the enhancement of the fraction of oscillators locked to the p...

We study large N behavior of the IIB matrix model using the equivalence between the IIB matrix model for finite N and a field theory on a non-commutative periodic lattice with N ×N sites. We find that the large N dependences of correlation functions can be obtained by naively counting the number of fields in the field theory on a non-commutative periodic lattice. Furthermore, the large N scalin...

The dynamics of a hysteretic relay oscillator with simple harmonic forcing is studied in this paper. Even though there are no bounded solutions in the absence of forcing, periodic excitation gives rise to more complex responses including periodic, quasi-periodic, and chaotic behavior. A Poincaré map is introduced to facilitate mathematical analysis. Families of period-one solutions are determin...

A generalized Hodgkin-Huxley model of excitable membranes is defined, and traveling wave solutions of the model are analyzed using singular perturbation methods in phase space. A complete classification determines whether a system exhibits finite wave train and periodic bursting behavior or only single pulse and regular periodic behavior. Qualitative properties of the bursts are deduced and use...

Simple periodic as well as more complex behaviors are shown to occur in the human pupil light reflex with piecewise constant mixed and delayed feedback. The output of an infrared video pupillometer, an analog voltage proportional to pupil area, is processed by an electronic comparator which synthesizes the piecewise constant feedback. The system is described by a nonlinear delay differential eq...

Abstract The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation the system results in periodic, quasi-periodic, chaotic and unbounded behavior. An explicit Poincaré map constructed an implicit constraint on switching time. stability fixed points corresponding to period-one solutions By varying parameters, we observed saddle-center pitchfork bifu...

This paper demonstrates how parsimonious models of sinusoidal functions can be used to fit spatially variant time series in which there is considerable variation of a periodic type. A typical shortcoming of such tools relates to the difficulty in capturing idiosyncratic variation in periodic models. The strategy developed here addresses this deficiency. While previous work has sought to overcom...

This article describes a concept for programming behavior based robots which combines properties of real-time operating systems with behavior-based programming to solve problems of scalability and reactivity. This new concept features hard and soft periodic processes, preemptive reflexes, behavior processes on different execution frequencies and a background process.