We consider a model of genetic network that has been previously presented by J. Lewis. This model takes the form of delay differential equations with two delays. We give conditions for the local stability of the non-trivial steady state. We investigate the condition under which stability is lost and oscillations occur. In particular, we show that when the ratio of the time delays passes a thres...

Movements of the hyobranchial apparatus in reptiles and amphibians contribute to many behaviors including feeding, lung ventilation, buccopharyngeal respiration, thermoregulation, olfaction, defense and display. In a semi-aquatic turtle, Platysternon megacephalum, x-ray video and airflow measurements from blowhole pneumotachography show no evidence that above water hyobranchial movements contri...

The occurrence of oscillations in a well-known asymptotic preserving (AP) numerical scheme is investigated in the context of a linear model of diffusive relaxation, known as the P1 equations. The scheme is derived with operator splitting methods that separate the P1 system into slow and fast dynamics. A careful analysis of the scheme shows that binary oscillations can occur as a result of a bla...

fertilization is triggered by changes in intracellular calcium concentration. in mammals, these transients in ooplasmic calcium concentration take the form of repetitive spikes, so called calcium oscillations (ca2+-oscillations). these oscillations are important for relieve of meiotic arrest and to induce all the other events of oocyte activation. although a surface mediated way of oocyte activ...

We review the Floquet theory of linear differential equations with periodic coefficients and discuss its applications to neutrino oscillations in matter of periodically varying density. In particular, we consider parametric resonance in neutrino oscillations which can occur in such media, and discuss implications for oscillations of neutrinos traversing the earth and passing through the earth's...

Gamma oscillations are thought to temporally link the activity of distributed cells. We discuss mechanisms of gamma oscillations in the hippocampus and review evidence supporting a functional role for such oscillations in several key hippocampal operations, including cell grouping, dynamic routing, and memory. We propose that memory encoding and retrieval are coordinated by different frequencie...

Fluctuating forces imposed on the airway smooth muscle due to breathing are believed to regulate hyperresponsiveness in vivo. However, recent animal and human isolated airway studies have shown that typical breathing-sized transmural pressure (Ptm) oscillations around a fixed mean are ineffective at mitigating airway constriction. To help understand this discrepancy, we hypothesized that Ptm os...

Neuroelectric oscillations reflect rhythmic shifting of neuronal ensembles between high and low excitability states. In natural settings, important stimuli often occur in rhythmic streams, and when oscillations entrain to an input rhythm their high excitability phases coincide with events in the stream, effectively amplifying neuronal input responses. When operating in a 'rhythmic mode', attent...

Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes a...