Abstract
We provide sufficient conditions for the existence of limit cycles for the Floquet differential equations x(t) = Ax(t) + ε(B(t)x(t) + b(t)), where x(t) and b(t) are column vectors of length n, A and B(t) are n × n matrices, the components of b(t) and B(t) are T-periodic functions, the differential equation x(t) = Ax(t) has a plane filled with T-periodic orbits, and ε is a small parameter. The proof of this result is based on averaging theory but only uses linear algebra.
Original language | English |
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Pages (from-to) | 1129-1136 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 19 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- Averaging theory
- Floquet differential equation
- Limit cycle
- Periodic solution