We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in R4 in resonance 1:n perturbed inside a class of piecewise linear differential systems, which appear in a natural way in control theory. Our main result shows that at most 1 limit cycle can bifurcate using expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed. © 2009 Elsevier Inc. All rights reserved.
|Journal||Applied Mathematics and Computation|
|Publication status||Published - 1 Sep 2009|
- Averaging method
- Control systems
- Limit cycles
- Resonance 1:n
Llibre, J., & Makhlouf, A. (2009). Bifurcation of limit cycles from a 4-dimensional center in 1:n resonance. Applied Mathematics and Computation, 215, 140-146. https://doi.org/10.1016/j.amc.2009.04.065