TY - JOUR
T1 - Existence of piecewise linear differential systems with exactly n limit cycles for all n ∈ ℕ
AU - Llibre, Jaume
AU - Ponce, Enrique
AU - Zhang, Xiang
PY - 2003/8/1
Y1 - 2003/8/1
N2 - In this paper, we prove that the piecewise linear differential system ẋ = - y - εφ(x), ẏ = x with ε ≠ 0 and φ an odd piecewise linear periodic function of period 4, has exactly n limit cycles in the strip |x| ≤ 2(n+1). Consequently, there are piecewise linear differential systems having infinitely many limit cycles in the real plane. We also provide examples of piecewise linear differential systems having exactly n limit cycles for all n ∈ ℕ. © 2003 Elsevier Science Ltd. All rights reserved.
AB - In this paper, we prove that the piecewise linear differential system ẋ = - y - εφ(x), ẏ = x with ε ≠ 0 and φ an odd piecewise linear periodic function of period 4, has exactly n limit cycles in the strip |x| ≤ 2(n+1). Consequently, there are piecewise linear differential systems having infinitely many limit cycles in the real plane. We also provide examples of piecewise linear differential systems having exactly n limit cycles for all n ∈ ℕ. © 2003 Elsevier Science Ltd. All rights reserved.
KW - Limit cycles
KW - Nonlinear oscillations
KW - Piecewise linear control system
UR - https://www.scopus.com/pages/publications/0038346051
U2 - 10.1016/S0362-546X(03)00122-6
DO - 10.1016/S0362-546X(03)00122-6
M3 - Article
SN - 0362-546X
VL - 54
SP - 977
EP - 994
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -