Homoclinic Bifurcations of the Merging Strange Attractors in the Lorenz-like System

TL;DR

This paper analytically identifies parameter regions in a Lorenz-like system where homoclinic orbits exist and numerically explores various bifurcation scenarios, revealing new complex dynamics.

Contribution

It provides the first analytical proof of homoclinic orbit existence in Lorenz-like systems with nonnegative saddle value and explores new bifurcation scenarios numerically.

Findings

Analytical proof of homoclinic orbit existence in specified parameter regions.

Numerical discovery of new bifurcation scenarios.

Identification of complex dynamical behaviors in Lorenz-like systems.

Abstract

In this article we construct the parameter region where the existence of a homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like system will be analytically proved in the case of a nonnegative saddle value. Then, for a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the detected parameter region is carried out to discover several new interesting bifurcation scenarios.