Bifurcations of relaxation oscillations

2004 ◽  
pp. 295-316 ◽  
Author(s):  
John Guckenheimer
Keyword(s):  
Relaxation Oscillations

Recurrent canards producing relaxation oscillations

2021 ◽  
Vol 31 (2) ◽  
pp. 023121
Author(s):  
C. Abdulwahed ◽  
F. Verhulst
Keyword(s):  
Relaxation Oscillations

Relaxation oscillations for Leslie-type predator–prey model with Holling Type I response functional function

2021 ◽  
Vol 120 ◽  
pp. 107328
Author(s):  
Shimin Li ◽  
Xiaoling Wang ◽  
Xiaoli Li ◽  
Kuilin Wu
Keyword(s):  
Type I ◽  
Relaxation Oscillations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Prolonged response of skeletal muscle in the absence of penetrating anions

1960 ◽  
Vol 198 (2) ◽  
pp. 289-299 ◽  
Author(s):  
Gertrude Falk ◽  
Jorge F. Landa
Keyword(s):  
Action Potentials ◽  
Critical Concentration ◽  
Relaxation Oscillations ◽  
Plateau Phase ◽  
Slow Oscillations ◽  
Mechanical Responses ◽  
External Potassium ◽  
Prolonged Response ◽  
Plateau Level ◽  
Potassium Addition

Replacement of Ringer's chloride by a variety of nonpenetrating anions results in prolonged electrical and mechanical responses of muscle to stimulation. The ‘negative after-potential’ is characterized by a slowly increasing secondary depolarization which reaches a stable plateau lasting as long as 2 minutes. After-discharge frequently occurs during early depolarization. In most fibers repolarization is relatively abrupt, but in some, slow oscillations resembling relaxation oscillations arise following the plateau, grow gradually in amplitude and, only when they are of sufficient amplitude, does the membrane repolarize. Prolonged depolarization can still be produced when the spike has failed. At times, fibers may respond with short-duration action potentials, but may be primed to give prolonged responses by previous stimuli or by increase of external potassium. Addition of chloride has no effect below a critical concentration. Reduction of sodium to 25% of normal does not change plateau level or duration. Duration of the plateau phase is decreased by potassium.

Information transmission by Marangoni-driven relaxation oscillations at droplets

Soft Matter ◽  
2018 ◽  
Vol 14 (45) ◽  
pp. 9250-9262 ◽  
Author(s):  
Marcel Mokbel ◽  
Karin Schwarzenberger ◽  
Sebastian Aland ◽  
Kerstin Eckert
Keyword(s):  
Information Transmission ◽  
Marangoni Flow ◽  
Relaxation Oscillations ◽  
A Chain

Via ensemble interaction, Marangoni flow transports a signal in the form of relaxation oscillations along a chain of sub-mm droplets.

scholarly journals Kinetic boundary friction

1947 ◽  
Vol 189 (1016) ◽  
pp. 88-102 ◽  
Keyword(s):  
Oleic Acid ◽  
Mineral Oil ◽  
Boundary Friction ◽  
Effect Of Temperature ◽  
Pure Substance ◽  
Relaxation Oscillations ◽  
Kinetic Friction ◽  
Fatty Oil ◽  
Frictional Forces ◽  
Kinetic Boundary

It is shown that the exhibition of smooth sliding and relaxation oscillations, or ‘stick-slips’, under conditions of boundary lubrication, when frictional forces are measured by the deflexion of an elastic system, may be explained as due to the dependence of kinetic friction on velocity. In the cases giving smooth sliding, kinetic friction decreases as velocity decreases, at very low speeds; for the cases giving relaxation oscillations kinetic friction increases as velocity decreases. That is, sliding under boundary conditions is not inherently discontinuous, any discontinuous motion being due to the dynamics of the measuring instrument, and is the result of kinetic friction increasing as velocity decreases. Curves of boundary friction against velocity, using various slicing surfaces, have been determined for a number of lubricants, which show both the above-mentioned types of friction-velocity relationship; and the dependence is shown of kinetic boundary friction on molecular weight for a series of esters of the fatty acids, on percentage of fatty oil in a compounded lubricant (actually oleic acid in mineral oil) and on temperature for a pure substance and a mineral oil. The measurements with the series of esters show some agreement with results given by Fogg (1940). The mixtures of oleic acid with mineral oil give decreasing kinetic friction with increasing percentage of oleic acid right up to 100% oleic acid. The effect of temperature on the dependence of friction in velocity shows that the temperature at which relaxation oscillations first occur depends on the speed of sliding, from which it appears that measurements of the temperature at which relaxation oscillations start at constant sliding speed (Frewing 1942) are not a measure of the temperature at which there is a discontinuity in the properties of the boundary layer.

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