Kolmogorov differential systems with prescribed algebraic limit cycles

Authors

  • Rima Chouader Laboratory of Applied Mathematics, Department of Mathematics, University of setif 1, 19000, Algeria
  • Salah Benyoucef Laboratory of Applied Mathematics, Department of Mathematics, University of setif 1, 19000, Algeria
  • Ahmed Bendjeddou Laboratory of Applied Mathematics, Department of Mathematics, University of setif 1, 19000, Algeria

Keywords:

Sixteenth problem of Hilbert, planar differential system, invariant curve, periodic solution, hyperbolic limit cycle.

Abstract

For a given algebraic curve, we exhibit Kolmogorov differential systems, and we show that these systems admit precisely the bounded components of the curve as hyperbolic limit cycles if certain conditions on the parameters of the system are satisfied.

Downloads

Published

2021-01-12

Issue

Vol. 18 No. 1 (2021)

Section

Differential equations, dynamical systems and optimal control