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 x = -y - epsilonphi(x), y = x with e 54 0 and 0 an odd piecewise linear periodic function of period 4, has exactly n limit cycles in the strip \x\ less than or equal to 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 E is an element of N. (C) 2003 Elsevier Science Ltd. All rights reserved.