Limit Cycles of Planar Quadratic Differential Equations,
Abstract
Since Hilbert posed the problem of systematically counting and locating the limite cycles of polynomial systems on the plane in 1900, much effort 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. This paper considers the class of quadratic differential equations which admit a unique equilibrium state, and establish sufficient conditions for the existence and uniqueness of limit cycles. The work is based upon insights and techniques developed in an earlier analysis of such systems motivated by questions from mathematical control theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1982
- Accession Number
- ADA120710
Entities
People
- Daniel E. Koditschek
- K. S. Narendra
Organizations
- Yale University