Saad Eddine Hamizi, Rachid Boukoucha
abstract:
This paper is devoted to the study of a family of planar polynomial differential
systems. First, we prove that the considered family has invariant algebraic
curves which are given explicitly. Then, we introduce an explicit expression for
their first integral. Moreover, we provide sufficient conditions for the systems
to possess two limit cycles explicitly given: one is an algebraic and the other
is shown to be non-algebraic. The applicability of our result was illustrated by
concrete examples.
Mathematics Subject Classification: 34C05, 34C07, 37C27, 37K10
Key words and phrases: Limit cycle, Riccati equation, invariant algebraic curve, first integral