Analytical search for homoclinic bifurcations in the Shimizu-Morioka model

The existence of a homoclinic butterfly to a saddle with zero saddle value is established analytically for the Shimizu-Morioka model.

► We study the existence of the Lorenz attractor in the Shimizu-Morioka model.
► We prove analytically the system has a homoclinic orbit.
► We use a refined method of comparison systems.