Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations

Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations

In this paper, we consider the family of generalized Abel equations of the form x ′ = A ( t ) x m + B ( t ) x n , where A ,  B are trigonometric polynomials and m , n ∈ N . We characterize the existence of non-trivial limit cycles in this family, in terms of the trigonometric monomials.

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Veröffentlicht in:Qualitative theory of dynamical systems 2021, Vol.20 (1), Article 15
Hauptverfasser: Álvarez, M. J., Bravo, J. L., Fernández, M., Prohens, R.
Format: Artikel
Sprache:eng
Schlagworte:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
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Zusammenfassung:In this paper, we consider the family of generalized Abel equations of the form x ′ = A ( t ) x m + B ( t ) x n , where A ,  B are trigonometric polynomials and m , n ∈ N . We characterize the existence of non-trivial limit cycles in this family, in terms of the trigonometric monomials.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-021-00450-4