Abel-like differential equations with a unique limit cycle
✍ Scribed by M.J. Álvarez; J.L. Bravo; M. Fernández
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 265 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0362-546X
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✦ Synopsis
For the family of scalar Abel-like equations
and k ≥ 1, we characterize the existence of non-trivial limit cycles (periodic solutions that are isolated in the set of periodic solutions different from the trivial x(t) ≡ 0) in terms of n, m, k, i l , j l , i b , j b .
📜 SIMILAR VOLUMES
We extend some previous results on the maximum number of isolated periodic solutions of generalized Abel equation and rigid systems. The key hypothesis is a monotonicity assumption on any stability operator (for instance, the divergence) along the solutions of a suitable transversal system. In such
Impulsive di erential equations arise frequently in the modelling of many physical systems whose states are subjects to sudden change at certain moments, for example, in population biology, the di usion of chemicals, the spread of heat, the radiation of electromagnetic waves, the maintenance of a sp