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| LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS |
| Yancong Xu,Tianzhu Lan,Zhenxue Wei |
| (Dept. of Math., Hangzhou Normal University, Hangzhou 310036, Zhejiang, PR China;School of Computer Science and Software Engineering, East China Normal University, 200062, Shanghai, PR China) |
| DOI： |
| Abstract: |
| Homoclinic snake always refers to the branches of homoclinic orbits \mbox{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. |
| Key words: round-snakes; round-isolas; normal form; Swift-Hohenberg equation; localized patterns |