An example of bifurcation to homoclinic orbits

Abstract Consider the equation x − x + x 2 = −λ 1 x + λ 2 ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ 1 , λ 2 ) is small. For λ = 0, there is a homoclinic orbit Γ through zero. For λ ≠ 0 and small, there can be “strange” attractors near Γ. The purpose of this paper is to determine the curves in λ-space of bifurcation to “strange” attractors and to relate this to hyperbolic subharmonic bifurcations.