2025-12-302025-12-302025TONON, Durval José; SANTOS, Mayk Joaquim dos; CRISTIANO, Rony. Melnikov functions of first and second order for 2-dimensional piecewise non-Hamiltonian systems with n regions. Publicationes Mathematicae Debrecen, Debrecen, v. 107, n. 1/2, p. 1-32, 2025. DOI: 10.5486/PMD.2025.9867. Disponível em: https://publi.math.unideb.hu/contents.php?szam=2025+%2F+107+%2F+1-2. Acesso em: 9 dez. 2025.0033 - 3883e- 2064 - 2849https://publi.math.unideb.hu/contents.php?szam=2025+%2F+107+%2F+1-2In this paper, we examine piecewise non-Hamiltonian systems where the switching manifold consists of n half straight lines ri originating from the origin, and each domain Di is bounded by two consecutive half straight lines ri and ri+1. Our main goal is to derive the expressions of the first- and second-order Melnikov functions. We address the question of the bifurcation of limit cycles in several interesting models by performing a first-order Melnikov analysis on (1) a buck power converter, (2) a Lotka–Volterra model, and (3) a piecewise smooth system with cubic vector fields. Additionally, we conduct a second-order Melnikov analysis on (4) a piecewise linear vector field with heteroclinic connections.engAcesso RestritoArtigo10.5486/PMD.2025.9867