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

Abstract

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
JournalNonlinearity
Volume30
Issue number5
DOIs
StatePublished - Mar 23 2017

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Square and bow-tie configurations in the cyclic evasion problem'. Together they form a unique fingerprint.

Cite this