A saddle-focus equilibrium with a homoclinic orbit generates infinite horseshoes when ρ < |λ| (Shilnikov condition), producing spiral-type chaos.
Shilnikov (1965): if a 3D system has a saddle-focus equilibrium with eigenvalues ρ±iω (unstable) and −λ (stable), and a homoclinic orbit returning to it, then ρ < λ implies a Smale horseshoe → chaos. The spiral trajectory winds infinitely many times near the fixed point.