We show how an island (isola) evolves out of the usual S-curve of steady states of diffusion flames when radiation losses are accounted for and how it eventually disappears when radiation increases further. At small activation temperatures there are never any islands. We show that stable oscillations evolve first out of perturbations of steady states on the S-curve at large Damköhler numbers. O...

In this paper, we study the oscillation of nonlinear fractional nabla difference equations of the form [Formula: see text]where c and α are constants, [Formula: see text] is the Riemann-Liouville fractional nabla difference operator of order [Formula: see text] is a real number, and [Formula: see text]. Some sufficient conditions for oscillation are established.

We consider a class of second-order Emden-Fowler equations with positive and nonpositve neutral coefficients. By using the Riccati transformation and inequalities, several oscillation and asymptotic results are established. Some examples are given to illustrate the main results.

We study the amplification of information transfer in excitable systems. We show that excitable systems residing in a steady state near a bifurcation point to complex oscillatory behavior incorporate several frequencies that can be exploited for a resonant amplification of information transfer. In particular, for excitable neurons that reside in a steady state near a bifurcation point to ellipt...

We present a combined theoretical and computational analysis of three-dimensional unsteady finite-Reynolds-number flows in collapsible tubes whose walls perform prescribed high-frequency oscillations which resemble those typically observed in experiments with a Starling resistor. Following an analysis of the flow fields, we investigate the system’s overall energy budget and establish the critic...

Systems of interacting cells containing a metabolic pathway with an autocatalytic reaction are investigated. The individual cells are considered to be identical and are described by differential equations proposed for the description of glycolytic oscillations. The coupling is realized by exchange of metabolites across the cell membranes. No constraints are introduced concerning the number of i...

We report on theoretical and experimental observations of self-sustained fast [gigahertz (GHz)] electronic oscillations resulting from coupled electron-photon dynamics in ultrahigh-Q Si microdisk resonators with cw pumping. Our theoretical analysis identifies conditions for generating steady-state GHz oscillations while suppressing thermal oscillations [megahertz (MHz)] with submilliwatt input ...

Neural oscillations are the intrinsic characteristics of brain activities. Traditional electrophysiological techniques (e.g., the steady-state evoked potential, SSEP) have provided important insights into the mechanisms of neural oscillations in the high frequency ranges (>1 Hz). However, the neural oscillations within the low frequency ranges (<1 Hz) and deep brain areas are rarely examined. B...