Abstract
Spatiotemporal periodic patterns, including phase-locked oscillations, mirror-reflecting waves, standing waves, in-phase or anti-phase oscillations are investigated in a ring of bidirectionally coupled oscillators with neutral delay feedback. It is confirmed that neutral feedback makes Hopf bifurcation occur in a larger domain of parameters. We calculate the normal forms near Hopf bifurcation, D N equivariant Hopf bifurcation and double-Hopf bifurcation in this neutral equation by using the method of multiple scales. Theoretically, the appearance of the in-phase, anti-phase and phase-locked oscillations that we observed in the simulation about a ring of delay coupled Hindmarsh-Rose neurons with neutral feedback is explained.
| Original language | English |
|---|---|
| Pages (from-to) | 1475-1492 |
| Number of pages | 18 |
| Journal | Nonlinear Dynamics |
| Volume | 73 |
| Issue number | 3 |
| DOIs | |
| State | Published - Aug 2013 |
Keywords
- Double-Hopf bifurcation
- Equivariant bifurcation
- Multiple scale
- Networks
- Neutral delay differential equations
- Synchronization
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