Limit Cycles of Planar Quadratic Differential Equations

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General Robotics, Automation, Sensing and Perception Laboratory
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Narendra, K. S.
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Since Hilbert posed the problem of systematically counting and locating lhe limit cycle of polynomial systems on the plane in 1900, much efTort has been expended in its investigation. A large body of literature - chiefly by Chinese and Soviet authors - has addressed this question in the context of differential equations whose field is specified by quadratic polynomials, In this paper we consider the class of quadratic differential equations which admit a unique equilibrium state, and establish sufficient conditions, algebraic in system coefficients, for the existence and uniqueness of a limit cycles. The work is based upon insights and techniques developed in an earlier analysis of such systems [1] motivated by questions from mathematical control theory.

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1984-03-01
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This is a post-print version. Published in Journal of Differential Equations, Volume 54, March 1984, pages 181-195. At the time of publication, author Daniel E. Koditschek was affliliated with Yale University. Currently, he is a faculty member in the School of Engineering at the University of Pennsylvania.
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