Yuan Xiao-feng, Guo Rui-hai. Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1067-1074.
Citation: Yuan Xiao-feng, Guo Rui-hai. Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1067-1074.

Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows

  • Received Date: 1990-10-22
  • Publish Date: 1991-12-15
  • This paper discusses the dynamic behavior of the Kelvin-Stuart cat's eye flow under periodic perturbations. By means of the Melnikov method the conditions to have bifurcations to subharmonics of even order for the oscillating orbits and to have bifurcations to subharmonics of any order for the rotating orbits are given, and further, the coexistence phenomena of the chaotic motions and periodic solutions are presented.
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    Langebartel,R.G.,Fourier expansions of rational fractions of elliptic integrals and Jacobian elliptic functions,SIAM.J.Math.Anal.,11,3(1980),506-513.
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    Guckenheimer,J.and P.Holmes,Nonlinear Oscillations,Dynamical Systems and Bifurcations of Vector Fields Springer-Verlag(1983).
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