A novel two‐parameter class of optimized hybrid block methods for integrating differential systems numerically †

Limit Cycles Bifurcating from a Period Annulus in Continuous Piecewise Linear Differential Systems with Three Zones

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127417500225 ◽

2017 ◽

Vol 27 (02) ◽

pp. 1750022 ◽

Cited By ~ 2

Author(s):

Maurício Firmino Silva Lima ◽

Claudio Pessoa ◽

Weber F. Pereira

Keyword(s):

Limit Cycles ◽

Vector Fields ◽

Poincaré Map ◽

Piecewise Linear ◽

Differential Systems ◽

Linear Vector ◽

Period Annulus ◽

Linear Differential Systems ◽

Linear Differential ◽

Two Parameter

We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits at least two limit cycles that appear by perturbations of a period annulus. Moreover, we describe the bifurcation of the limit cycles for this class through two examples of two-parameter families of piecewise linear vector fields with three zones.

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Some results of the Barbier-Chalonge-Divan system of stellar classification

Symposium - International Astronomical Union ◽

10.1017/s0074180900053250 ◽

1966 ◽

Vol 24 ◽

pp. 77-90 ◽

Cited By ~ 1

Author(s):

D. Chalonge

Keyword(s):

Early Type ◽

Parameter System ◽

Early Type Stars ◽

Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

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Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good

Zeitschrift für Sozialpsychologie ◽

10.1024//0044-3514.32.3.133 ◽

2001 ◽

Vol 32 (3) ◽

pp. 133-141 ◽

Cited By ~ 4

Author(s):

Gerrit Antonides ◽

Sophia R. Wunderink

Keyword(s):

Willingness To Pay ◽

Energy Saving ◽

Subjective Time ◽

Durable Good ◽

Discount Function ◽

Hyperbolic Discount ◽

The One ◽

Two Parameter ◽

Difference Effect ◽

Better Than

Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.

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