Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay
Articles
Rina Su
Northeast Forestry University
Chunrui Zhang
Northeast Forestry University
https://orcid.org/0000-0002-9356-5064
Published 2021-05-01
https://doi.org/10.15388/namc.2021.26.23050
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Keywords

Toda oscillators
normal form
Hopf-zero

How to Cite

Su R. and Zhang C. (2021) “Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay”, Nonlinear Analysis: Modelling and Control, 26(3), pp. 375-395. doi: 10.15388/namc.2021.26.23050.

Abstract

In this paper, the Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay was explored. First, the conditions of the occurrence of Hopf-zero bifurcation were obtained by analyzing the distribution of eigenvalues in correspondence to linearization. Second, the stability of Hopf-zero bifurcation periodic solutions was determined based on the discussion of the normal form of the system, and some numerical simulations were employed to illustrate the results of this study. Lastly, the normal form of the system on the center manifold was derived by using the center manifold theorem and normal form method.

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