Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems

Z.T. Zhusubaliyev, Erik Mosekilde

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The purpose of this Letter is to show how a border-collision bifurcation in a piecewise-smooth dynamical system can produce a direct transition from a stable equilibrium point to a two-dimensional invariant torus. Considering a system of nonautonomous differential equations describing the behavior of a power electronic DC/DC converter, we first determine the chart of dynamical modes and show that there is a region of parameter space in which the system has a single stable equilibrium point. Under variation of the parameters, this equilibrium may collide with a discontinuity boundary between two smooth regions in phase space. When this happens, one can observe a number of different bifurcation scenarios. One scenario is the continuous transformation of the stable equilibrium into a stable period-1 cycle. Another is the transformation of the stable equilibrium into an unstable period-1 cycle with complex conjugate multipliers, and the associated formation of a two-dimensional (ergodic or resonant) torus.
Original languageEnglish
JournalPhysics Letters A
Volume372
Issue number13
Pages (from-to)2237-2246
ISSN0375-9601
DOIs
Publication statusPublished - 2008

Keywords

  • equilibrium point
  • quasiperiodicity
  • piecewise-smooth systems
  • two-dimensional torus
  • border-collision bifurcations

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