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.

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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

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Autonomous Systems
  • Control Theory
  • Coordinate Systems
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Guarantees
  • Inequalities
  • Intervals
  • Linear Algebra
  • Polynomials
  • Spectra
  • Systems Science
  • Tank Guns
  • Trajectories

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Linear Algebra
  • Strategic Security Studies