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Received March 3, 2020; Accepted July 6, 2020; Published August 1, 2020
Abstract. With the help of the Bernoulli equation, we establish a new class of planar polynomial vector field of the form:
where are homogeneous polynomials of degrees and , respectively with . We prove that this class of differential systems has at most one explicit limit cycle. We obtain our result by giving a general class of differential systems of degree five with explicit non algebraic limit cycles.
How to Cite this Article:
Rebiha Benterki, A class of planar polynomial vector field with explicit non-algebraic limit cycles, Communications in Optimization Theory, Vol. 2020 (2020), Article ID 17, pp. 1-8.