A simple solution to the Braga-Mello conjecture

TL;DR

This paper proves the Braga-Mello conjecture, showing that for any natural number n, there exists a piecewise linear system with two zones in the plane having exactly n limit cycles, supported by explicit examples.

Contribution

The paper provides a proof of the Braga-Mello conjecture and offers explicit examples illustrating the location and stability of the limit cycles.

Findings

Proof of the Braga-Mello conjecture for all natural numbers n

Construction of explicit examples with specified limit cycles

Analysis of the location and stability of the limit cycles

Abstract

Recently Braga and Mello conjectured that for a given natural number n there is a piecewise linear system with two zones in the plane with exactly n limit cycles. In this paper we prove a result from which the conjecture is an immediate consequence. Several explicit examples are given where location and stability of limit cycles are provided.