Normal form solutions of dynamical systems in the basin of attraction of their fixed points

Tassos Bountis, George Tsarouhas, Russell Herman

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

The normal form theory of Poincaré, Siegel and Arnol'd is applied to an analytically solvable Lotka-Volterra system in the plane, and a periodically forced, dissipative Duffing's equation with chaotic orbits in its 3-dimensional phase space. For the planar model, we determine exactly how the convergence region of normal forms about a nodal fixed point is limited by the presence of singularities of the solutions in the complex t-plane. Despite such limitations, however, we show, in the case of a periodically driven system, that normal forms can be used to obtain useful estimates of the basin of attraction of a stable fixed point of the Poincaré map, whose "boundary" is formed by the intersecting invariant manifolds of a second hyperbolic fixed point nearby.

Original languageEnglish
Pages (from-to)34-50
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Volume33
Issue number1-3
DOIs
Publication statusPublished - Jan 1 1988

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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