Asymptotic Stability on Slow Time Scales for Periodic Systems

1981 ◽  
Vol 41 (1) ◽  
pp. 16-28 ◽  
Author(s):  
Stephen C. Persek
Keyword(s):  
Asymptotic Stability ◽  
Time Scales ◽  
Periodic Systems ◽  
Slow Time

Nonlinear acoustic forces acting on inhomogeneous fluids at slow time-scales

2016 ◽  
Vol 139 (4) ◽  
pp. 2152-2152 ◽  
Author(s):  
Jonas T. Karlsen ◽  
Per Augustsson ◽  
Henrik Bruus
Keyword(s):  
Time Scales ◽  
Slow Time ◽  
Inhomogeneous Fluids ◽  
Nonlinear Acoustic

scholarly journals Local postsynaptic signalling on slow time scales in reciprocal olfactory bulb granule cell spines matches asynchronous release

2020 ◽  
Author(s):  
Tiffany Ona Jodar ◽  
Vanessa Lage-Rupprecht ◽  
Nixon M. Abraham ◽  
Christine R. Rose ◽  
Veronica Egger
Keyword(s):  
Olfactory Bulb ◽  
Time Scales ◽  
Time Course ◽  
Granule Cells ◽  
Gaba Release ◽  
Fluorescence Signal ◽  
Slow Time ◽  
Triggered Release ◽  
Time To Peak ◽  
Adult Mice

AbstractIn the vertebrate olfactory bulb (OB), axonless granule cells (GC) mediate self- and lateral inhibitory interactions between mitral/tufted cells via reciprocal dendrodendritic synapses. Locally triggered release of GABA from the large reciprocal GC spines occurs on both fast and slow time scales, possibly enabling parallel processing during olfactory perception. Here we investigate local mechanisms for asynchronous spine output.To reveal the temporal and spatial characteristics of postsynaptic ion transients, we imaged spine and adjacent dendrite Ca2+- and Na+-signals with minimal exogenous buffering by the respective fluorescent indicator dyes upon two-photon uncaging of DNI-glutamate in OB slices from juvenile rats. Both postsynaptic fluorescence signals decayed slowly, with average half durations in the spine head of t1/2_Δ[Ca2+]i ~500 ms and t1/2_Δ[Na+]i ~1000 ms. We also analysed the kinetics of already existing data of postsynaptic spine Ca2+-signals in response to glomerular stimulation in OB slices from adult mice, either WT or animals with partial GC glutamate receptor deletions (NMDAR: GluN1 subunit; AMPAR: GluA2 subunit). In a large subset of spines the fluorescence signal had a protracted rise time (average time to peak ~400 ms, range 20 ms - >1000 ms). This slow rise was independent of Ca2+ entry via NMDARs, since similarly slow signals occurred in ΔGluN1 GCs. Additional Ca2+ entry in ΔGluA2 GCs (with AMPARs rendered Ca2+-permeable), however, resulted in larger ΔF/Fs that rose yet more slowly.Thus GC spines appear to dispose of several local mechanisms to promote asynchronous GABA release, which are reflected in the time course of mitral/tufted cell recurrent inhibition.

scholarly journals Local Postsynaptic Signaling on Slow Time Scales in Reciprocal Olfactory Bulb Granule Cell Spines Matches Asynchronous Release

2020 ◽  
Vol 12 ◽  
Author(s):  
Tiffany Ona Jodar ◽  
Vanessa Lage-Rupprecht ◽  
Nixon M. Abraham ◽  
Christine R. Rose ◽  
Veronica Egger
Keyword(s):  
Olfactory Bulb ◽  
Time Scales ◽  
Granule Cell ◽  
Slow Time ◽  
Asynchronous Release

scholarly journals Slow time scales in a dense vibrofluidized granular material

2020 ◽  
Vol 102 (1) ◽  
Author(s):  
Andrea Plati ◽  
Andrea Puglisi
Keyword(s):  
Granular Material ◽  
Time Scales ◽  
Slow Time

scholarly journals REDUCTION OF SLOW–FAST PERIODIC SYSTEMS WITH APPLICATIONS TO POPULATION DYNAMICS MODELS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250025 ◽  
Author(s):  
M. MARVÁ ◽  
J.-C. POGGIALE ◽  
R. BRAVO DE LA PARRA
Keyword(s):  
Time Scales ◽  
Species Interactions ◽  
Three Dimensional ◽  
Periodic Systems ◽  
Dimensional System ◽  
Predator Prey Model ◽  
Sir Epidemic ◽  
The Difference ◽  
Population Dynamics Models ◽  
The One

This work deals with the approximate reduction of a nonautonomous two time scales ordinary differential equations system with periodic fast dynamics. We illustrate this technique with the analysis of two models belonging to different fields in ecology. On the one hand, we deal with a two patches periodic predator–prey model with a refuge for prey. Considering migrations between patches to be faster than local interaction allows us to study a three-dimensional system by means of a two-dimensional one. On the other hand, a two time scales periodic eco-epidemic model is addressed by considering two competing species, one of them being affected by a periodic SIR epidemic process which is faster than inter-species interactions. The difference between time scales allows us to study the asymptotic behavior of the four-dimensional system by means of a planar, reduced one. Furthermore, we propose a methodology straightforwardly applicable to a very large class of two time scales periodic systems.

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