TY - JOUR
T1 - Bifurcation of limit cycles from a four-dimensional center in control systems
AU - Buicǎ, Adriana
AU - Llibre, Jaume
PY - 2005/1/1
Y1 - 2005/1/1
N2 - We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that three is an upper bound for the number of limit cycles, up to first-order expansion of the displacement function with respect to the small parameter. Moreover, this upper bound is reached. For proving this result we use the averaging method in a form where the differentiability of the system is not needed. © World Scientific Publishing Company.
AB - We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that three is an upper bound for the number of limit cycles, up to first-order expansion of the displacement function with respect to the small parameter. Moreover, this upper bound is reached. For proving this result we use the averaging method in a form where the differentiability of the system is not needed. © World Scientific Publishing Company.
KW - Four-dimensional control system
KW - Limit cycles
KW - Piecewise linear differential systems
U2 - 10.1142/S0218127405013599
DO - 10.1142/S0218127405013599
M3 - Article
SN - 0218-1274
VL - 15
SP - 2653
EP - 2662
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
IS - 8
ER -