Existence of piecewise linear differential systems with exactly n limit cycles for all n ∈ ℕ

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.