Ian Melbourne's Publication List

Publications on Heteroclinic Cycles

1. M. Krupa and I. Melbourne. Asymptotic stability of heteroclinic cycles in systems with symmetry, II.
   Proc. Roy. Soc. Edinburgh A 134A (2004) 1177-1197. (abstract, pdf file)

2. I. Melbourne, M. R. E. Proctor and A. M. Rucklidge. A heteroclinic model of geodynamo reversals and excursions.
   Dynamo and Dynamics, a Mathematical Challenge (P. Chossat et al. eds.) Kluwer, Netherlands, 2001, 363-370. (abstract, pdf)

3. P. Chossat, M. Krupa, I. Melbourne and A. Scheel. Magnetic dynamos in rotating convection --- A dynamical systems approach.
   Dynamics of Continuous, Discrete and Impulsive Systems 5 (1999) 327-340. ( abstract, pdf file )

4. P. Chossat, M. Krupa, I. Melbourne and A. Scheel. Transverse bifurcations of heteroclinic cycles in symmetric systems.
   Physica D 100 (1997) 85-100. ( abstract , pdf file )

5. M. Krupa and I. Melbourne. Asymptotic stability of heteroclinic cycles in systems with symmetry.
   Ergodic Theory Dyn. Syst. 15 (1995) 121-147. ( abstract , pdf file )

6. M. Krupa and I. Melbourne. Nonasymptotically stable attractors in O(2) mode interactions.
   Normal Forms and Homoclinic Chaos (W. Langford and W. Nagata eds.) Fields Institute Communications 4, Amer. Math. Soc., Providence, RI, 1995, 219-232. ( abstract , pdf file )

7. I. Melbourne. An example of a non-asymptotically stable attractor.
   Nonlinearity 4 (1991) 835-844 ( abstract )

8. I. Melbourne, P. Chossat and M. Golubitsky. Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry.
   Proc. Roy. Soc. Edinburgh 113A (1989) 315-345. Also in New Directions in Differential Equations and Dynamical Systems J.M. Ball ed. Roy. Soc. Edinburgh (1991) ( abstract )

9. I. Melbourne. Intermittency as a codimension three phenomenon.
   J. Dyn. Diff. Eqn. 1 (1989) 347-367. ( abstract )