Journal
APPLIED MATHEMATICS AND NONLINEAR SCIENCES
Volume 6, Issue 1, Pages 373-380Publisher
WALTER DE GRUYTER GMBH
DOI: 10.2478/AMNS.2020.2.00079
Keywords
periodic orbit; third-order differential equation; averaging theory; memory oscilators
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Funding
- Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigacion (FEDER) [MTM2016-77278-P]
- Agencia de Gestio d'Ajuts Universitaris i de Recerca grant [2017SGR1617]
- H2020 European Research Council [MSCA-RISE-2017-777911]
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Sufficient conditions are provided for the existence of periodic solutions in differential systems, which are often encountered in scientific and engineering problems.
We provide sufficient conditions for the existence of periodic solutions for the differential systems x' = y, y' = z, z' = -y - epsilon F(t, x, y, z), and x' = y, y' = -x - epsilon G(t, x, y, z, u), z' = u, u' = -z - epsilon H(t, x, y, z, u) where F, G and H are 2 pi-periodic functions in the variable t and epsilon is a small parameter. These differential systems appear frequently in many problems coming from the sciences and the engineering.
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