Square and bow-tie configurations in the cyclic evasion problem

M. D. Arnold, M. Golich, A. Grim, L. Vargas, V. Zharnitsky

Research output: Contribution to journalArticlepeer-review


Cyclic evasion of four agents on the plane is considered. There are two stationary shapes of configurations: square and degenerate bow-tie. The bow-tie is asymptotically attracting while the square is of focus-center type. Normal form analysis shows that square is nonlinearly unstable. The stable manifold consists of parallelograms that all converge to the square configuration. Based on these observations and numerical simulations, it is conjectured that any non-parallelogram non-degenerate configuration converges to the bow-tie.

Original languageEnglish (US)
Pages (from-to)1773-1787
Number of pages15
Issue number5
StatePublished - Mar 23 2017


  • Lyapunov functions
  • cyclic evasion
  • normal forms Mathematics Subject Classification numbers: 34D20
  • stability

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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