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.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 1 Aug 2003|
- Limit cycles
- Nonlinear oscillations
- Piecewise linear control system