Periodic solutions and bifurcation structure at high R in the Lorenz model
Abstract
A stable periodic solution of a Lorenz system (describing convection in a circular fluid loop and the behavior of a modified homopolar dynamo) in the limit R approaches infinity is computed as a fixed point of a Poincare mapping. The solution is shown to exist for finite R by application of the implicit function theorem. Successive bifurcations as R is decreased to the nonperiodic regime are investigated numerically.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 June 1979
 Bibcode:
 1979SJAM...36..457R
 Keywords:

 Branching (Mathematics);
 Mathematical Models;
 Periodic Functions;
 Poincare Spheres;
 Convective Flow;
 Cylindrical Bodies;
 Elliptic Functions;
 Homopolar Generators;
 Integral Equations;
 Loops;
 Fluid Mechanics and Heat Transfer