Multiple bifurcation analysis in a ring of delay coupled oscillators with neutral feedback

作者：Niu, Ben^*; Guo, Yuxiao; Wang, Hongbin

来源：Nonlinear Dynamics, 2013, 73(3): 1475-1492.

DOI：10.1007/s11071-013-0878-8

• Networks
• Neutral delay differential equations
• Multiple scale
• Equivariant bifurcation
• Double-Hopf bifurcation
• Synchronization

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.

• 出版日期2013-8
• 单位哈尔滨工业大学; 哈尔滨学院