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BISTABLE CHAOS .2. BIFURCATION-ANALYSIS
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UNSPECIFIED (1992) BISTABLE CHAOS .2. BIFURCATION-ANALYSIS. PHYSICAL REVIEW A, 46 (6). pp. 3100-3110. ISSN 1050-2947.
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Abstract
Results of a bifurcation analysis are given for the model of a Van der Pol-Duffing autonomous electronic oscillator. The oscillator is described by three ordinary differential equations and consists of a RC oscillator resistively coupled to an LC oscillator. The steady-state problem is described by the unfolding of the quartic potential F = 1/4X4 - 1/2alphaX2 + muX, giving rise to the elementary cusp catastrophe. We show how the bifurcation diagram evolves with mu and recover a "cross-shaped diagram" reminiscent of the one obtained by Boissonade and De Kepper for the Belousov-Zhabotinskii chemical system [J. Phys. Chem. 84, 501 (1980)]. We also show that nonzero values of mu result in coexisting attractors with different dynamics. Specifically, we show a limit cycle attractor in one potential well coexisting with a chaotic attractor in the other well.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Journal or Publication Title: | PHYSICAL REVIEW A | ||||
Publisher: | AMERICAN PHYSICAL SOC | ||||
ISSN: | 1050-2947 | ||||
Official Date: | 15 September 1992 | ||||
Dates: |
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Volume: | 46 | ||||
Number: | 6 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 3100-3110 | ||||
Publication Status: | Published |
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