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Analysis of stationary points and their bifurcations in the ABC-flow

Author

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  • Didov, A.A.
  • Uleysky, M.Yu.

Abstract

Analytical expressions for coordinates of stationary points and conditions for their existence in the ABC-flow are received. The type of the stationary points is shown analytically to be saddle-node. Exact expressions for eigenvalues and eigenvectors of the stability matrix are given. Behavior of the stationary points along the bifurcation lines is described.

Suggested Citation

  • Didov, A.A. & Uleysky, M.Yu., 2018. "Analysis of stationary points and their bifurcations in the ABC-flow," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 56-64.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:56-64
    DOI: 10.1016/j.amc.2018.02.032
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    References listed on IDEAS

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    1. Ershkov, Sergey V., 2016. "About existence of stationary points for the Arnold–Beltrami–Childress (ABC) flow," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 379-383.
    2. Ershkov, Sergey V., 2016. "Non-stationary helical flows for incompressible 3D Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 611-614.
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