Study of Poincare map and limit cycles for non-smooth Welander's system

TL;DR

This paper analyzes the non-smooth Welander's ocean convection model, focusing on the Poincare map and bifurcation of stable limit cycles, providing analytical insights into its dynamical behavior.

Contribution

It offers the first analytical study of bifurcations and limit cycles in the non-smooth version of Welander's ocean convection model.

Findings

Demonstrates bifurcation of a stable limit cycle

Analyzes the Poincare map for the non-smooth system

Identifies the existence of an escaping segment surrounding the limit cycle

Abstract

In this work, our primary goal is to study the Poincare map and the existence of limit cycles for Welander's 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 Poincare Map, we demonstrate analytically the bifurcation of a stable limit cycle surrounding an escaping segment.