Shilnikov condition: chaos occurs when γ/ρ > 1 (saddle-focus). The homoclinic orbit spirals into the equilibrium along stable manifold, then shoots out along the unstable one — creating Smale horseshoes.
ρ/ω defines the spiral tightness; γ the outgoing eigenvalue. When γ > ρ, infinitely many periodic orbits coexist with chaos.