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A new proof of the absence of limit cycles in a quadratic autonomous system
Published online by Cambridge University Press: 09 April 2009
Abstract
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The absence of limit cycles in the system (S): x′ = − y + dx2 + exy + fy2, y′ = x, (′ ≡ d/dt), for 0 ≦ f2 < 2, was shown by Yeh et al. (1963). The general case was established by Kukles and Šakhova using various special results and relying on an extraneous auxiliary system. In this paper we give a new proof of the theorem; in it, we draw mainly on the basic properties of the characteristic exponent of a cycle and use an intrinsic system, viz. the case d = − f(≠ 0) of (S) as an auxiliary system.
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- Copyright © Australian Mathematical Society 1977
References
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