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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

      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
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}

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