Multiple bifurcation analysis in a ring of delay coupled oscillators with neutral feedback |
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Authors: | Ben Niu Yuxiao Guo Hongbin Wang |
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Institution: | 1. Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, 150080, China 2. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
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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. |
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