Study of Poincaré Map and limit cycles for non-smooth Welander's Ocean Convection Model

In this work, our primary goal is to study the Poincaré Map and the existence of limit cycles for the Welander model that describes ocean convection. Welander developed two versions of his model, one with a smooth transition between convective states, and one with an abrupt non-smooth change. Our focus in this paper is to study the non-smooth model. Approaching through the Poincaré Map, we demonstrate analytically the bifurcation of a unique stable crossing limit cycle surrounding an escaping segment. In addition, we demonstrate that there is no sliding limit cycle.