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- Title
Multiple scales and normal forms in a ring of delay coupled oscillators with application to chaotic Hindmarsh-Rose neurons.
- Authors
Guo, Yuxiao; Jiang, Weihua; Niu, Ben
- Abstract
We study the appearance and stability of spatiotemporal periodic patterns like phase-locked oscillations, mirror-reflecting waves, standing waves, in-phase or antiphase oscillations, and coexistence of multiple patterns, in a ring of bidirectionally delay coupled oscillators. Hopf bifurcation, Hopf-Hopf bifurcation, and the equivariant Hopf bifurcation are studied in the viewpoint of normal forms obtained by using the method of multiple scales which is a kind of perturbation technique, thus a clear bifurcation scenario is depicted. We find time delay significantly affects the dynamics and induces rich spatiotemporal patterns. With the help of the unfolding system near Hopf-Hopf bifurcation, it is confirmed in some regions two kinds of stable oscillations may coexist. These phenomena are shown for the delay coupled limit cycle oscillators as well as for the delay coupled chaotic Hindmarsh-Rose neurons.
- Subjects
SPATIOTEMPORAL processes; PARAMETRONS; HOPF bifurcations; UNIDIMENSIONAL unfolding model; OSCILLATIONS
- Publication
Nonlinear Dynamics, 2013, Vol 71, Issue 3, p515
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-012-0678-6