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Planar Dynamics for Mixed Homogeneous Systems

Read, John (1996) Planar Dynamics for Mixed Homogeneous Systems. [Preprint]

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      Abstract

      A function $f_k:2rr$ is said to be [positively] homogeneous of order $k>0$ if $f_k(tx,ty)=t^kf_k(x,y)$ for all $(x,y)rr^2$ and all $trr [$t0$]. We investigate dynamics in the $(x,y)-$plane governed by right hand sides defined in terms of (positively) homogeneous functions of degrees $m$ and $n$. Thus, $x$ will be homogeneous of degree $m$ and $y$ will be homogeneous of degree $n$. Specifically, we determine necessary and sufficient conditions that the origin be a center (or focus). For all other dynamics we then determine necessary and sufficient conditions for the stability of the origin by constructing a Lyopunov function.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Subjects: 34-xx Ordinary differential equations > 34Cxx Qualitative theory
      34-xx Ordinary differential equations > 34Axx General theory
      34-xx Ordinary differential equations > 34Dxx Stability theory
      70-xx Mechanics of particles and systems > 70Kxx Nonlinear dynamics
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 24 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/159

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