Homoclinic snake always refers to the branches of homoclinic orbits near a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this pape...Homoclinic snake always refers to the branches of homoclinic orbits near a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms （non-reversible term and non-k-symmetry term） are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so- called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.展开更多
基金supported by the National NSF of China(No.11671114)
文摘Homoclinic snake always refers to the branches of homoclinic orbits near a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms （non-reversible term and non-k-symmetry term） are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so- called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.
