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# Limit Cycles of Planar Quadratic Differential Equations

Daniel E. Koditschek*, K. S. Narendra†

*: University of Pennsylvania

†: Yale University

Full PDF | Penn ScholarlyCommons

Abstract |

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. |

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. |

BibTeX entry |

article{Koditschek1984181},
title = {Limit cycles of planar quadratic differential equations },
journal = {Journal of Differential Equations },
volume = {54},
number = {2},
pages = {181 - 195},
year = {1984},
note = {},
issn = {0022-0396},
doi = {http://dx.doi.org/10.1016/0022-0396(84)90157-8},
url = {http://www.sciencedirect.com/science/article/pii/0022039684901578},
author = {D.E Koditschek and K.S Narendra}
} |