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Nonuniqueness of stable limit cycles in a class of enzyme catalyzed reactions

โœ Scribed by Dieter Erle

Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
261 KB
Volume
82
Category
Article
ISSN
0022-247X

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๐Ÿ“œ SIMILAR VOLUMES

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In this paper a class of quadratic systems is studied. By quadratic systems we mean autonomous quadratic vector fields in the plane. The class under consideration is class \(\mathrm{II}_{n=0}\) in the Chinese classification of quadratic systems. Bifurcation sets \(\delta=\delta^{*}(l, m)(m>2, l>0)\)

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A perturbation method has been used to prove that in the reversible Selkov model, a model describing glycolytic oscillations, the limit cycles emerging at the Hopf points are stable asymptotically within a range of parameter values.

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โœ W.T. Vanhorssen; R.E. Kooij ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 861 KB

Within the class of quadratic perturbations we show analytically or numerically how many limit cycles can be bifurcated at first order out of the periodic orbits nested around the centre point in \((0,0)\) or nested around the centre point in \((0,1 / n)\) of the quadratic system \(\dot{x}=-y+n y^{2